(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 10.3' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. For additional information concerning CDF *) (* licensing and redistribution see: *) (* *) (* www.wolfram.com/cdf/adopting-cdf/licensing-options.html *) (* *) (*************************************************************************) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 1064, 20] NotebookDataLength[ 83520, 1517] NotebookOptionsPosition[ 82518, 1489] NotebookOutlinePosition[ 82896, 1505] CellTagsIndexPosition[ 82853, 1502] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Exponential Growth and Decay", "Title", CellChangeTimes->{{3.533724116105065*^9, 3.5337241245285463`*^9}, { 3.5448043653286557`*^9, 3.544804370262938*^9}, {3.545517457548363*^9, 3.5455174581303964`*^9}, {3.6491589303613043`*^9, 3.649158943331046*^9}, { 3.6624875858023806`*^9, 3.662487587942797*^9}}, Background->RGBColor[ 1, 0.85, 0.85],ExpressionUUID->"aadb28ff-e1a3-4f9c-be54-ca0a6a18e55f"], Cell[TextData[{ "The function that models the exponential growth or decay of a quantity is \ the same as that for continuous compounding, which is exponential growth of \ money: A = P", Cell[BoxData[ FormBox[ SuperscriptBox["e", "rt"], TraditionalForm]],ExpressionUUID-> "83a9d9dc-b843-4cd5-93d3-bb8a05f40485"], ". \n\nIn general, the exponential (uninhibited) growth or decay of ANY \ quantity is given by\n\n", StyleBox["A = C", FontFamily->"Arial", FontSize->28, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ FormBox[ SuperscriptBox["e", "rt"], TraditionalForm]], FontFamily->"Arial", FontSize->28, FontColor->RGBColor[1, 0, 0],ExpressionUUID-> "c807aa0b-3f49-4ccd-81de-6ef37526ada8"], ", \n", StyleBox["where A is the amount after time t, \nC is the initial amount, \nr \ is the growth (+) or decay (-) constant", FontSlant->"Italic"] }], "Section", CellChangeTimes->{{3.5337241397124147`*^9, 3.5337243422469993`*^9}, { 3.5337243760209312`*^9, 3.533724419121396*^9}, {3.5337244536213694`*^9, 3.533724460120741*^9}, 3.6625621903012843`*^9, {3.6628418437560635`*^9, 3.662841847270393*^9}}, TextAlignment->Center, Background->RGBColor[ 0.87, 0.94, 1],ExpressionUUID->"ef8f9916-3e52-4676-8d05-d4a7d1473861"], Cell[CellGroupData[{ Cell[TextData[{ "\n", StyleBox["Question 1:", FontVariations->{"Underline"->True}], " Population growth may be described as exponential within a certain \ domain. Consider the population of U.S. states from the 1790 census until \ the 2000 census. Which states (and over what domain) have population that \ seem to grow linearly? Exponentially?\n\na. Check the boxes for Kentucky \ and Maine. Describe the population growth in these states for the 200-year \ period from 1800 until 2000. Provide a mathematical equation that models the \ population growth for each state.\n\nb. Now check the boxes for Virginia and \ Arizona. Describe the population growth in these states for the 200-year \ period from 1800 until 2000. Provide a mathematical equation that models the \ population growth for each state.\n\nc. Click the boxes to show the \ population growth for several other states. Name 3 states whose population \ growth seem to NOT follow linear or exponential growth models. 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Range[50]; $CellContext`override$$ = "neutral"]; If[ And[$CellContext`override$$ === "none", $CellContext`x =!= {}], $CellContext`x = {}; \ $CellContext`override$$ = "neutral"]; If[$CellContext`begin$$ + $CellContext`duration$$ > 2000, $CellContext`duration$$ = 2000 - $CellContext`begin$$]; If[$CellContext`x =!= {}, $CellContext`f$$[ Map[Tooltip[ Apply[List, Select[ Part[#, 2], Function[$CellContext`datum$, $CellContext`begin$$ <= Part[$CellContext`datum$, 1] <= $CellContext`begin$$ + $CellContext`duration$$]], {1}], Part[#, 1]]& , Part[$CellContext`statePopulationRules, $CellContext`x]]], Graphics[{}, Frame -> True, ImageSize -> {590, 200}, AspectRatio -> 200/590, ImagePadding -> {{60, 10}, {40, 10}}]]), "Specifications" :> {{{$CellContext`f$$, ListLinePlot[#, PlotRange -> All, ImageSize -> {590, 200}, AspectRatio -> 200/590, Axes -> False, Frame -> True, FrameLabel -> {"census", "population"}, ImagePadding -> {{60, 10}, {40, 10}}]& , "visualization function"}, {( ListLinePlot[#, 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"Labeled"}, "show these states", Dynamic[$CellContext`x = Range[50]; Pane[ CheckboxBar[ Dynamic[$CellContext`x], Thread[Range[50] -> $CellContext`stateList]], {590, 160}]], {{$CellContext`override$$, "neutral"}, { "all", "none", "neutral"}}}, "Options" :> {AutorunSequencing -> {1, 2, 3}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{576., {244., 250.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(({$CellContext`x = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50}, $CellContext`statePopulationRules = { "Alabama" -> { 1790 -> 0, 1800 -> 1250, 1810 -> 9046, 1820 -> 127901, 1830 -> 309527, 1840 -> 590756, 1850 -> 771623, 1860 -> 964201, 1870 -> 996992, 1880 -> 1262505, 1890 -> 1513401, 1900 -> 1828697, 1910 -> 2138093, 1920 -> 2348174, 1930 -> 2646248, 1940 -> 2832961, 1950 -> 3061743, 1960 -> 3266740, 1970 -> 3444354, 1980 -> 3894025, 1990 -> 4040587, 2000 -> 4461130}, "Alaska" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 0, 1880 -> 33426, 1890 -> 32052, 1900 -> 63592, 1910 -> 64356, 1920 -> 55036, 1930 -> 59278, 1940 -> 72524, 1950 -> 128643, 1960 -> 226167, 1970 -> 302853, 1980 -> 401851, 1990 -> 550043, 2000 -> 628933}, "Arizona" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 9658, 1880 -> 40440, 1890 -> 88243, 1900 -> 122931, 1910 -> 204354, 1920 -> 334162, 1930 -> 435573, 1940 -> 499261, 1950 -> 749587, 1960 -> 1302161, 1970 -> 1775399, 1980 -> 2716546, 1990 -> 3665228, 2000 -> 5140683}, "Arkansas" -> { 1790 -> 0, 1800 -> 0, 1810 -> 1062, 1820 -> 14273, 1830 -> 30388, 1840 -> 97574, 1850 -> 209897, 1860 -> 435450, 1870 -> 484471, 1880 -> 802525, 1890 -> 1128211, 1900 -> 1311564, 1910 -> 1574449, 1920 -> 1752204, 1930 -> 1854482, 1940 -> 1949387, 1950 -> 1909511, 1960 -> 1786272, 1970 -> 1923322, 1980 -> 2286357, 1990 -> 2350725, 2000 -> 2679733}, "California" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 92597, 1860 -> 379994, 1870 -> 560247, 1880 -> 864694, 1890 -> 1213398, 1900 -> 1485053, 1910 -> 2377549, 1920 -> 3426861, 1930 -> 5677251, 1940 -> 6907387, 1950 -> 10586223, 1960 -> 15717204, 1970 -> 19971069, 1980 -> 23667764, 1990 -> 29760021, 2000 -> 33930798}, "Colorado" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 34277, 1870 -> 39864, 1880 -> 194327, 1890 -> 413249, 1900 -> 539700, 1910 -> 799024, 1920 -> 939629, 1930 -> 1035791, 1940 -> 1123296, 1950 -> 1325089, 1960 -> 1753947, 1970 -> 2209596, 1980 -> 2889735, 1990 -> 3294394, 2000 -> 4311882}, "Connecticut" -> { 1790 -> 237946, 1800 -> 251002, 1810 -> 261942, 1820 -> 275248, 1830 -> 297675, 1840 -> 309978, 1850 -> 370792, 1860 -> 460147, 1870 -> 537454, 1880 -> 622700, 1890 -> 746258, 1900 -> 908420, 1910 -> 1114756, 1920 -> 1380631, 1930 -> 1606903, 1940 -> 1709242, 1950 -> 2007280, 1960 -> 2535234, 1970 -> 3032217, 1980 -> 3107564, 1990 -> 3287116, 2000 -> 3409535}, "Delaware" -> { 1790 -> 59096, 1800 -> 64273, 1810 -> 72674, 1820 -> 72749, 1830 -> 76748, 1840 -> 78085, 1850 -> 91532, 1860 -> 112216, 1870 -> 125015, 1880 -> 146608, 1890 -> 168493, 1900 -> 184735, 1910 -> 202322, 1920 -> 223003, 1930 -> 230380, 1940 -> 266505, 1950 -> 318085, 1960 -> 446292, 1970 -> 548104, 1980 -> 594338, 1990 -> 666168, 2000 -> 785068}, "Florida" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 34730, 1840 -> 54477, 1850 -> 87445, 1860 -> 140424, 1870 -> 187748, 1880 -> 269493, 1890 -> 391422, 1900 -> 528542, 1910 -> 752619, 1920 -> 968470, 1930 -> 1468211, 1940 -> 1897414, 1950 -> 2771305, 1960 -> 4951560, 1970 -> 6791418, 1980 -> 9746961, 1990 -> 12937926, 2000 -> 16028890}, "Georgia" -> { 1790 -> 82548, 1800 -> 162686, 1810 -> 252433, 1820 -> 340989, 1830 -> 516823, 1840 -> 691392, 1850 -> 906185, 1860 -> 1057286, 1870 -> 1184109, 1880 -> 1542180, 1890 -> 1837353, 1900 -> 2216331, 1910 -> 2609121, 1920 -> 2895832, 1930 -> 2908506, 1940 -> 3123723, 1950 -> 3444578, 1960 -> 3943116, 1970 -> 4587930, 1980 -> 5462982, 1990 -> 6478216, 2000 -> 8206975}, "Hawaii" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 0, 1880 -> 0, 1890 -> 0, 1900 -> 154001, 1910 -> 191874, 1920 -> 225881, 1930 -> 368300, 1940 -> 422770, 1950 -> 499794, 1960 -> 632772, 1970 -> 769913, 1980 -> 964691, 1990 -> 1108229, 2000 -> 1216642}, "Idaho" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 14999, 1880 -> 32610, 1890 -> 88548, 1900 -> 161772, 1910 -> 325594, 1920 -> 431866, 1930 -> 445032, 1940 -> 524873, 1950 -> 588637, 1960 -> 667191, 1970 -> 713015, 1980 -> 944127, 1990 -> 1006749, 2000 -> 1297274}, "Illinois" -> { 1790 -> 0, 1800 -> 0, 1810 -> 12282, 1820 -> 55211, 1830 -> 157445, 1840 -> 476183, 1850 -> 851470, 1860 -> 1711951, 1870 -> 2539891, 1880 -> 3077871, 1890 -> 3826352, 1900 -> 4821550, 1910 -> 5638591, 1920 -> 6485280, 1930 -> 7630654, 1940 -> 7897241, 1950 -> 8712176, 1960 -> 10081158, 1970 -> 11110285, 1980 -> 11427409, 1990 -> 11430602, 2000 -> 12439042}, "Indiana" -> { 1790 -> 0, 1800 -> 5641, 1810 -> 24520, 1820 -> 147718, 1830 -> 343031, 1840 -> 685866, 1850 -> 988416, 1860 -> 1350428, 1870 -> 1680637, 1880 -> 1978301, 1890 -> 2192404, 1900 -> 2516462, 1910 -> 2700876, 1920 -> 2930390, 1930 -> 3238503, 1940 -> 3427796, 1950 -> 3934224, 1960 -> 4662498, 1970 -> 5195392, 1980 -> 5490210, 1990 -> 5544159, 2000 -> 6090782}, "Iowa" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 43112, 1850 -> 192914, 1860 -> 674913, 1870 -> 1194020, 1880 -> 1624615, 1890 -> 1912297, 1900 -> 2231853, 1910 -> 2224771, 1920 -> 2404021, 1930 -> 2470939, 1940 -> 2538268, 1950 -> 2621073, 1960 -> 2757537, 1970 -> 2825368, 1980 -> 2913808, 1990 -> 2776755, 2000 -> 2931923}, "Kansas" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 107206, 1870 -> 364399, 1880 -> 996096, 1890 -> 1428108, 1900 -> 1470495, 1910 -> 1690949, 1920 -> 1769257, 1930 -> 1880999, 1940 -> 1801028, 1950 -> 1905299, 1960 -> 2178611, 1970 -> 2249071, 1980 -> 2364236, 1990 -> 2477574, 2000 -> 2693824}, "Kentucky" -> { 1790 -> 73677, 1800 -> 220955, 1810 -> 406511, 1820 -> 564317, 1830 -> 687917, 1840 -> 779828, 1850 -> 982405, 1860 -> 1155684, 1870 -> 1321011, 1880 -> 1648690, 1890 -> 1858635, 1900 -> 2147174, 1910 -> 2289905, 1920 -> 2416630, 1930 -> 2614589, 1940 -> 2845627, 1950 -> 2944806, 1960 -> 3038156, 1970 -> 3220711, 1980 -> 3660324, 1990 -> 3685296, 2000 -> 4049431}, "Louisiana" -> { 1790 -> 0, 1800 -> 0, 1810 -> 76556, 1820 -> 153407, 1830 -> 215739, 1840 -> 352411, 1850 -> 517762, 1860 -> 708002, 1870 -> 726915, 1880 -> 939946, 1890 -> 1118588, 1900 -> 1381625, 1910 -> 1656388, 1920 -> 1798509, 1930 -> 2101593, 1940 -> 2363880, 1950 -> 2683516, 1960 -> 3257022, 1970 -> 3644637, 1980 -> 4206116, 1990 -> 4219973, 2000 -> 4480271}, "Maine" -> { 1790 -> 96540, 1800 -> 151719, 1810 -> 228705, 1820 -> 298335, 1830 -> 399455, 1840 -> 501793, 1850 -> 583169, 1860 -> 628279, 1870 -> 626915, 1880 -> 648936, 1890 -> 661086, 1900 -> 694466, 1910 -> 742371, 1920 -> 768014, 1930 -> 797423, 1940 -> 847226, 1950 -> 913774, 1960 -> 969265, 1970 -> 993722, 1980 -> 1125043, 1990 -> 1227928, 2000 -> 1277731}, "Maryland" -> { 1790 -> 319728, 1800 -> 341548, 1810 -> 380546, 1820 -> 407350, 1830 -> 447040, 1840 -> 470019, 1850 -> 583034, 1860 -> 687049, 1870 -> 780894, 1880 -> 934943, 1890 -> 1042390, 1900 -> 1188044, 1910 -> 1295346, 1920 -> 1499661, 1930 -> 1631526, 1940 -> 1821244, 1950 -> 2343001, 1960 -> 3100689, 1970 -> 3923897, 1980 -> 4216933, 1990 -> 4781468, 2000 -> 5307886}, "Massachusetts" -> { 1790 -> 378787, 1800 -> 422845, 1810 -> 472040, 1820 -> 523287, 1830 -> 610408, 1840 -> 737699, 1850 -> 994514, 1860 -> 1231066, 1870 -> 1457351, 1880 -> 1783085, 1890 -> 2238947, 1900 -> 2805346, 1910 -> 3366416, 1920 -> 3852356, 1930 -> 4249614, 1940 -> 4316721, 1950 -> 4690514, 1960 -> 5148578, 1970 -> 5689170, 1980 -> 5737093, 1990 -> 6016425, 2000 -> 6355568}, "Michigan" -> { 1790 -> 0, 1800 -> 0, 1810 -> 4762, 1820 -> 8896, 1830 -> 31639, 1840 -> 212267, 1850 -> 397654, 1860 -> 749113, 1870 -> 1184059, 1880 -> 1636937, 1890 -> 2093890, 1900 -> 2420982, 1910 -> 2810173, 1920 -> 3668412, 1930 -> 4842325, 1940 -> 5256106, 1950 -> 6371766, 1960 -> 7823194, 1970 -> 8881826, 1980 -> 9262044, 1990 -> 9295297, 2000 -> 9955829}, "Minnesota" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 6077, 1860 -> 172023, 1870 -> 439706, 1880 -> 780773, 1890 -> 1310283, 1900 -> 1751394, 1910 -> 2075708, 1920 -> 2387125, 1930 -> 2563953, 1940 -> 2792300, 1950 -> 2982483, 1960 -> 3413864, 1970 -> 3806103, 1980 -> 4075970, 1990 -> 4375099, 2000 -> 4925670}, "Mississippi" -> { 1790 -> 0, 1800 -> 7600, 1810 -> 31306, 1820 -> 75448, 1830 -> 136621, 1840 -> 375651, 1850 -> 606526, 1860 -> 791305, 1870 -> 827922, 1880 -> 1131597, 1890 -> 1289600, 1900 -> 1551270, 1910 -> 1797114, 1920 -> 1790618, 1930 -> 2009821, 1940 -> 2183796, 1950 -> 2178914, 1960 -> 2178141, 1970 -> 2216994, 1980 -> 2520770, 1990 -> 2573216, 2000 -> 2852927}, "Missouri" -> { 1790 -> 0, 1800 -> 0, 1810 -> 19783, 1820 -> 66586, 1830 -> 140455, 1840 -> 383702, 1850 -> 682044, 1860 -> 1182012, 1870 -> 1721295, 1880 -> 2168380, 1890 -> 2679185, 1900 -> 3106665, 1910 -> 3293335, 1920 -> 3404055, 1930 -> 3629367, 1940 -> 3784664, 1950 -> 3954653, 1960 -> 4319813, 1970 -> 4677623, 1980 -> 4916766, 1990 -> 5117073, 2000 -> 5606260}, "Montana" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 20595, 1880 -> 39159, 1890 -> 142924, 1900 -> 243329, 1910 -> 376053, 1920 -> 548889, 1930 -> 537606, 1940 -> 559456, 1950 -> 591024, 1960 -> 674767, 1970 -> 694409, 1980 -> 786690, 1990 -> 799065, 2000 -> 905316}, "Nebraska" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 28841, 1870 -> 122993, 1880 -> 452402, 1890 -> 1062656, 1900 -> 1066300, 1910 -> 1192214, 1920 -> 1296372, 1930 -> 1377963, 1940 -> 1315834, 1950 -> 1325510, 1960 -> 1411330, 1970 -> 1485333, 1980 -> 1569825, 1990 -> 1578385, 2000 -> 1715369}, "Nevada" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 6857, 1870 -> 42491, 1880 -> 62266, 1890 -> 47355, 1900 -> 42335, 1910 -> 81875, 1920 -> 77407, 1930 -> 91058, 1940 -> 110247, 1950 -> 160083, 1960 -> 285278, 1970 -> 488738, 1980 -> 800508, 1990 -> 1201833, 2000 -> 2002032}, "New Hampshire" -> { 1790 -> 141885, 1800 -> 183858, 1810 -> 214460, 1820 -> 244161, 1830 -> 269328, 1840 -> 284574, 1850 -> 317976, 1860 -> 326073, 1870 -> 318300, 1880 -> 346991, 1890 -> 376530, 1900 -> 411588, 1910 -> 430572, 1920 -> 443083, 1930 -> 465293, 1940 -> 491524, 1950 -> 533242, 1960 -> 606921, 1970 -> 737681, 1980 -> 920610, 1990 -> 1109252, 2000 -> 1238415}, "New Jersey" -> { 1790 -> 184139, 1800 -> 211149, 1810 -> 245562, 1820 -> 277575, 1830 -> 320823, 1840 -> 373306, 1850 -> 489555, 1860 -> 672035, 1870 -> 906096, 1880 -> 1131116, 1890 -> 1444933, 1900 -> 1883669, 1910 -> 2537167, 1920 -> 3155900, 1930 -> 4041334, 1940 -> 4160165, 1950 -> 4835329, 1960 -> 6066782, 1970 -> 7171112, 1980 -> 7365011, 1990 -> 7730188, 2000 -> 8424354}, "New Mexico" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 61547, 1860 -> 93516, 1870 -> 91874, 1880 -> 119565, 1890 -> 160282, 1900 -> 195310, 1910 -> 327301, 1920 -> 360350, 1930 -> 423317, 1940 -> 531818, 1950 -> 681187, 1960 -> 951023, 1970 -> 1017055, 1980 -> 1303302, 1990 -> 1515069, 2000 -> 1823821}, "New York" -> { 1790 -> 340120, 1800 -> 589051, 1810 -> 959049, 1820 -> 1372812, 1830 -> 1918608, 1840 -> 2428921, 1850 -> 3097394, 1860 -> 3880735, 1870 -> 4382759, 1880 -> 5082871, 1890 -> 6003174, 1900 -> 7268894, 1910 -> 9113614, 1920 -> 10385227, 1930 -> 12588066, 1940 -> 13479142, 1950 -> 14830192, 1960 -> 16782304, 1970 -> 18241391, 1980 -> 17558165, 1990 -> 17990455, 2000 -> 19004973}, "North Carolina" -> { 1790 -> 393751, 1800 -> 478103, 1810 -> 555500, 1820 -> 638829, 1830 -> 737987, 1840 -> 753419, 1850 -> 869039, 1860 -> 992622, 1870 -> 1071361, 1880 -> 1399750, 1890 -> 1617949, 1900 -> 1893810, 1910 -> 2206287, 1920 -> 2559123, 1930 -> 3170276, 1940 -> 3571623, 1950 -> 4061929, 1960 -> 4556155, 1970 -> 5084411, 1980 -> 5880095, 1990 -> 6628637, 2000 -> 8067673}, "North Dakota" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 2405, 1880 -> 36909, 1890 -> 190983, 1900 -> 319146, 1910 -> 577056, 1920 -> 646872, 1930 -> 680845, 1940 -> 641935, 1950 -> 619636, 1960 -> 632446, 1970 -> 617792, 1980 -> 652717, 1990 -> 638800, 2000 -> 643756}, "Ohio" -> { 1790 -> 0, 1800 -> 45365, 1810 -> 230760, 1820 -> 581434, 1830 -> 937903, 1840 -> 1519467, 1850 -> 1980329, 1860 -> 2339511, 1870 -> 2665260, 1880 -> 3198062, 1890 -> 3672329, 1900 -> 4157545, 1910 -> 4767121, 1920 -> 5759394, 1930 -> 6646697, 1940 -> 6907612, 1950 -> 7946627, 1960 -> 9706397, 1970 -> 10657423, 1980 -> 10797603, 1990 -> 10847115, 2000 -> 11374540}, "Oklahoma" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 0, 1880 -> 0, 1890 -> 258657, 1900 -> 790391, 1910 -> 1657155, 1920 -> 2028283, 1930 -> 2396040, 1940 -> 2336434, 1950 -> 2233351, 1960 -> 2328284, 1970 -> 2559463, 1980 -> 3025487, 1990 -> 3145585, 2000 -> 3458819}, "Oregon" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 12093, 1860 -> 52465, 1870 -> 90923, 1880 -> 174768, 1890 -> 317704, 1900 -> 413536, 1910 -> 672765, 1920 -> 783389, 1930 -> 953786, 1940 -> 1089684, 1950 -> 1521341, 1960 -> 1768687, 1970 -> 2091533, 1980 -> 2633156, 1990 -> 2842321, 2000 -> 3428543}, "Pennsylvania" -> { 1790 -> 434373, 1800 -> 602365, 1810 -> 810091, 1820 -> 1049458, 1830 -> 1348233, 1840 -> 1724033, 1850 -> 2311786, 1860 -> 2906215, 1870 -> 3521951, 1880 -> 4282891, 1890 -> 5258113, 1900 -> 6302115, 1910 -> 7665111, 1920 -> 8720017, 1930 -> 9631350, 1940 -> 9900180, 1950 -> 10498012, 1960 -> 11319366, 1970 -> 11800766, 1980 -> 11864720, 1990 -> 11881643, 2000 -> 12300670}, "Rhode Island" -> { 1790 -> 68825, 1800 -> 69122, 1810 -> 76931, 1820 -> 83059, 1830 -> 97199, 1840 -> 108830, 1850 -> 147545, 1860 -> 174620, 1870 -> 217353, 1880 -> 276531, 1890 -> 345506, 1900 -> 428556, 1910 -> 542610, 1920 -> 604397, 1930 -> 687497, 1940 -> 713346, 1950 -> 791896, 1960 -> 859488, 1970 -> 949723, 1980 -> 947154, 1990 -> 1003464, 2000 -> 1049662}, "South Carolina" -> { 1790 -> 249073, 1800 -> 345591, 1810 -> 415115, 1820 -> 502741, 1830 -> 581185, 1840 -> 594398, 1850 -> 668507, 1860 -> 703708, 1870 -> 705606, 1880 -> 995577, 1890 -> 1151149, 1900 -> 1340316, 1910 -> 1515400, 1920 -> 1683724, 1930 -> 1738765, 1940 -> 1899804, 1950 -> 2117027, 1960 -> 2382594, 1970 -> 2590713, 1980 -> 3120729, 1990 -> 3486703, 2000 -> 4025061}, "South Dakota" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 4837, 1870 -> 11776, 1880 -> 98268, 1890 -> 348600, 1900 -> 401570, 1910 -> 583888, 1920 -> 636547, 1930 -> 692849, 1940 -> 642961, 1950 -> 652740, 1960 -> 680514, 1970 -> 666257, 1980 -> 690768, 1990 -> 696004, 2000 -> 756874}, "Tennessee" -> { 1790 -> 35691, 1800 -> 105602, 1810 -> 261727, 1820 -> 422823, 1830 -> 681904, 1840 -> 829210, 1850 -> 1002717, 1860 -> 1109801, 1870 -> 1258520, 1880 -> 1542359, 1890 -> 1767518, 1900 -> 2020616, 1910 -> 2184789, 1920 -> 2337885, 1930 -> 2616556, 1940 -> 2915841, 1950 -> 3291718, 1960 -> 3567089, 1970 -> 3926018, 1980 -> 4591023, 1990 -> 4877185, 2000 -> 5700037}, "Texas" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 212592, 1860 -> 604215, 1870 -> 818579, 1880 -> 1591749, 1890 -> 2235527, 1900 -> 3048710, 1910 -> 3896542, 1920 -> 4663228, 1930 -> 5824715, 1940 -> 6414824, 1950 -> 7711194, 1960 -> 9579677, 1970 -> 11198655, 1980 -> 14225513, 1990 -> 16986510, 2000 -> 20903994}, "Utah" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 11380, 1860 -> 40273, 1870 -> 86786, 1880 -> 143963, 1890 -> 210779, 1900 -> 276749, 1910 -> 373351, 1920 -> 449396, 1930 -> 507847, 1940 -> 550310, 1950 -> 688862, 1960 -> 890627, 1970 -> 1059273, 1980 -> 1461037, 1990 -> 1722850, 2000 -> 2236714}, "Vermont" -> { 1790 -> 85425, 1800 -> 154465, 1810 -> 217895, 1820 -> 235981, 1830 -> 280652, 1840 -> 291948, 1850 -> 314120, 1860 -> 315098, 1870 -> 330551, 1880 -> 332286, 1890 -> 332422, 1900 -> 343641, 1910 -> 355956, 1920 -> 352428, 1930 -> 359611, 1940 -> 359231, 1950 -> 377747, 1960 -> 389881, 1970 -> 444732, 1980 -> 511456, 1990 -> 562758, 2000 -> 609890}, "Virginia" -> { 1790 -> 691737, 1800 -> 807557, 1810 -> 877683, 1820 -> 938261, 1830 -> 1044054, 1840 -> 1025227, 1850 -> 1119348, 1860 -> 1219630, 1870 -> 1225163, 1880 -> 1512565, 1890 -> 1655980, 1900 -> 1854184, 1910 -> 2061612, 1920 -> 2309187, 1930 -> 2421851, 1940 -> 2677773, 1950 -> 3318680, 1960 -> 3966949, 1970 -> 4651448, 1980 -> 5346797, 1990 -> 6187358, 2000 -> 7100702}, "Washington" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 1201, 1860 -> 11594, 1870 -> 23955, 1880 -> 75116, 1890 -> 357232, 1900 -> 518103, 1910 -> 1141990, 1920 -> 1356621, 1930 -> 1563396, 1940 -> 1736191, 1950 -> 2378963, 1960 -> 2853214, 1970 -> 3413244, 1980 -> 4132353, 1990 -> 4866692, 2000 -> 5908684}, "West Virginia" -> { 1790 -> 55873, 1800 -> 78592, 1810 -> 105469, 1820 -> 136808, 1830 -> 176924, 1840 -> 224537, 1850 -> 302313, 1860 -> 376688, 1870 -> 442014, 1880 -> 618457, 1890 -> 762794, 1900 -> 958800, 1910 -> 1221119, 1920 -> 1463701, 1930 -> 1729205, 1940 -> 1901974, 1950 -> 2005552, 1960 -> 1860421, 1970 -> 1744237, 1980 -> 1950186, 1990 -> 1793477, 2000 -> 1813077}, "Wisconsin" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 30945, 1850 -> 305391, 1860 -> 775881, 1870 -> 1054670, 1880 -> 1315497, 1890 -> 1693330, 1900 -> 2069042, 1910 -> 2333860, 1920 -> 2632067, 1930 -> 2939006, 1940 -> 3137587, 1950 -> 3434575, 1960 -> 3951777, 1970 -> 4417821, 1980 -> 4705642, 1990 -> 4891769, 2000 -> 5371210}, "Wyoming" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 9118, 1880 -> 20789, 1890 -> 62555, 1900 -> 92531, 1910 -> 145965, 1920 -> 194402, 1930 -> 225565, 1940 -> 250742, 1950 -> 290529, 1960 -> 330066, 1970 -> 332416, 1980 -> 469557, 1990 -> 453588, 2000 -> 495304}}, $CellContext`stateList = { "Alabama", "Alaska", "Arizona", "Arkansas", "California", "Colorado", "Connecticut", "Delaware", "Florida", "Georgia", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine", "Maryland", "Massachusetts", "Michigan", "Minnesota", "Mississippi", "Missouri", "Montana", "Nebraska", "Nevada", "New Hampshire", "New Jersey", "New Mexico", "New York", "North Carolina", "North Dakota", "Ohio", "Oklahoma", "Oregon", "Pennsylvania", "Rhode Island", "South Carolina", "South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia", "Washington", "West Virginia", "Wisconsin", "Wyoming"}}; Typeset`initDone$$ = True); ReleaseHold[ HoldComplete[{$CellContext`statePopulationRules = Sort[{"Maine" -> { 1790 -> 96540, 1800 -> 151719, 1810 -> 228705, 1820 -> 298335, 1830 -> 399455, 1840 -> 501793, 1850 -> 583169, 1860 -> 628279, 1870 -> 626915, 1880 -> 648936, 1890 -> 661086, 1900 -> 694466, 1910 -> 742371, 1920 -> 768014, 1930 -> 797423, 1940 -> 847226, 1950 -> 913774, 1960 -> 969265, 1970 -> 993722, 1980 -> 1125043, 1990 -> 1227928, 2000 -> 1277731}, "New Hampshire" -> { 1790 -> 141885, 1800 -> 183858, 1810 -> 214460, 1820 -> 244161, 1830 -> 269328, 1840 -> 284574, 1850 -> 317976, 1860 -> 326073, 1870 -> 318300, 1880 -> 346991, 1890 -> 376530, 1900 -> 411588, 1910 -> 430572, 1920 -> 443083, 1930 -> 465293, 1940 -> 491524, 1950 -> 533242, 1960 -> 606921, 1970 -> 737681, 1980 -> 920610, 1990 -> 1109252, 2000 -> 1238415}, "Vermont" -> { 1790 -> 85425, 1800 -> 154465, 1810 -> 217895, 1820 -> 235981, 1830 -> 280652, 1840 -> 291948, 1850 -> 314120, 1860 -> 315098, 1870 -> 330551, 1880 -> 332286, 1890 -> 332422, 1900 -> 343641, 1910 -> 355956, 1920 -> 352428, 1930 -> 359611, 1940 -> 359231, 1950 -> 377747, 1960 -> 389881, 1970 -> 444732, 1980 -> 511456, 1990 -> 562758, 2000 -> 609890}, "Massachusetts" -> { 1790 -> 378787, 1800 -> 422845, 1810 -> 472040, 1820 -> 523287, 1830 -> 610408, 1840 -> 737699, 1850 -> 994514, 1860 -> 1231066, 1870 -> 1457351, 1880 -> 1783085, 1890 -> 2238947, 1900 -> 2805346, 1910 -> 3366416, 1920 -> 3852356, 1930 -> 4249614, 1940 -> 4316721, 1950 -> 4690514, 1960 -> 5148578, 1970 -> 5689170, 1980 -> 5737093, 1990 -> 6016425, 2000 -> 6355568}, "Rhode Island" -> { 1790 -> 68825, 1800 -> 69122, 1810 -> 76931, 1820 -> 83059, 1830 -> 97199, 1840 -> 108830, 1850 -> 147545, 1860 -> 174620, 1870 -> 217353, 1880 -> 276531, 1890 -> 345506, 1900 -> 428556, 1910 -> 542610, 1920 -> 604397, 1930 -> 687497, 1940 -> 713346, 1950 -> 791896, 1960 -> 859488, 1970 -> 949723, 1980 -> 947154, 1990 -> 1003464, 2000 -> 1049662}, "Connecticut" -> { 1790 -> 237946, 1800 -> 251002, 1810 -> 261942, 1820 -> 275248, 1830 -> 297675, 1840 -> 309978, 1850 -> 370792, 1860 -> 460147, 1870 -> 537454, 1880 -> 622700, 1890 -> 746258, 1900 -> 908420, 1910 -> 1114756, 1920 -> 1380631, 1930 -> 1606903, 1940 -> 1709242, 1950 -> 2007280, 1960 -> 2535234, 1970 -> 3032217, 1980 -> 3107564, 1990 -> 3287116, 2000 -> 3409535}, "New York" -> { 1790 -> 340120, 1800 -> 589051, 1810 -> 959049, 1820 -> 1372812, 1830 -> 1918608, 1840 -> 2428921, 1850 -> 3097394, 1860 -> 3880735, 1870 -> 4382759, 1880 -> 5082871, 1890 -> 6003174, 1900 -> 7268894, 1910 -> 9113614, 1920 -> 10385227, 1930 -> 12588066, 1940 -> 13479142, 1950 -> 14830192, 1960 -> 16782304, 1970 -> 18241391, 1980 -> 17558165, 1990 -> 17990455, 2000 -> 19004973}, "New Jersey" -> { 1790 -> 184139, 1800 -> 211149, 1810 -> 245562, 1820 -> 277575, 1830 -> 320823, 1840 -> 373306, 1850 -> 489555, 1860 -> 672035, 1870 -> 906096, 1880 -> 1131116, 1890 -> 1444933, 1900 -> 1883669, 1910 -> 2537167, 1920 -> 3155900, 1930 -> 4041334, 1940 -> 4160165, 1950 -> 4835329, 1960 -> 6066782, 1970 -> 7171112, 1980 -> 7365011, 1990 -> 7730188, 2000 -> 8424354}, "Pennsylvania" -> { 1790 -> 434373, 1800 -> 602365, 1810 -> 810091, 1820 -> 1049458, 1830 -> 1348233, 1840 -> 1724033, 1850 -> 2311786, 1860 -> 2906215, 1870 -> 3521951, 1880 -> 4282891, 1890 -> 5258113, 1900 -> 6302115, 1910 -> 7665111, 1920 -> 8720017, 1930 -> 9631350, 1940 -> 9900180, 1950 -> 10498012, 1960 -> 11319366, 1970 -> 11800766, 1980 -> 11864720, 1990 -> 11881643, 2000 -> 12300670}, "Ohio" -> { 1790 -> 0, 1800 -> 45365, 1810 -> 230760, 1820 -> 581434, 1830 -> 937903, 1840 -> 1519467, 1850 -> 1980329, 1860 -> 2339511, 1870 -> 2665260, 1880 -> 3198062, 1890 -> 3672329, 1900 -> 4157545, 1910 -> 4767121, 1920 -> 5759394, 1930 -> 6646697, 1940 -> 6907612, 1950 -> 7946627, 1960 -> 9706397, 1970 -> 10657423, 1980 -> 10797603, 1990 -> 10847115, 2000 -> 11374540}, "Indiana" -> { 1790 -> 0, 1800 -> 5641, 1810 -> 24520, 1820 -> 147718, 1830 -> 343031, 1840 -> 685866, 1850 -> 988416, 1860 -> 1350428, 1870 -> 1680637, 1880 -> 1978301, 1890 -> 2192404, 1900 -> 2516462, 1910 -> 2700876, 1920 -> 2930390, 1930 -> 3238503, 1940 -> 3427796, 1950 -> 3934224, 1960 -> 4662498, 1970 -> 5195392, 1980 -> 5490210, 1990 -> 5544159, 2000 -> 6090782}, "Illinois" -> { 1790 -> 0, 1800 -> 0, 1810 -> 12282, 1820 -> 55211, 1830 -> 157445, 1840 -> 476183, 1850 -> 851470, 1860 -> 1711951, 1870 -> 2539891, 1880 -> 3077871, 1890 -> 3826352, 1900 -> 4821550, 1910 -> 5638591, 1920 -> 6485280, 1930 -> 7630654, 1940 -> 7897241, 1950 -> 8712176, 1960 -> 10081158, 1970 -> 11110285, 1980 -> 11427409, 1990 -> 11430602, 2000 -> 12439042}, "Michigan" -> { 1790 -> 0, 1800 -> 0, 1810 -> 4762, 1820 -> 8896, 1830 -> 31639, 1840 -> 212267, 1850 -> 397654, 1860 -> 749113, 1870 -> 1184059, 1880 -> 1636937, 1890 -> 2093890, 1900 -> 2420982, 1910 -> 2810173, 1920 -> 3668412, 1930 -> 4842325, 1940 -> 5256106, 1950 -> 6371766, 1960 -> 7823194, 1970 -> 8881826, 1980 -> 9262044, 1990 -> 9295297, 2000 -> 9955829}, "Wisconsin" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 30945, 1850 -> 305391, 1860 -> 775881, 1870 -> 1054670, 1880 -> 1315497, 1890 -> 1693330, 1900 -> 2069042, 1910 -> 2333860, 1920 -> 2632067, 1930 -> 2939006, 1940 -> 3137587, 1950 -> 3434575, 1960 -> 3951777, 1970 -> 4417821, 1980 -> 4705642, 1990 -> 4891769, 2000 -> 5371210}, "Minnesota" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 6077, 1860 -> 172023, 1870 -> 439706, 1880 -> 780773, 1890 -> 1310283, 1900 -> 1751394, 1910 -> 2075708, 1920 -> 2387125, 1930 -> 2563953, 1940 -> 2792300, 1950 -> 2982483, 1960 -> 3413864, 1970 -> 3806103, 1980 -> 4075970, 1990 -> 4375099, 2000 -> 4925670}, "Iowa" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 43112, 1850 -> 192914, 1860 -> 674913, 1870 -> 1194020, 1880 -> 1624615, 1890 -> 1912297, 1900 -> 2231853, 1910 -> 2224771, 1920 -> 2404021, 1930 -> 2470939, 1940 -> 2538268, 1950 -> 2621073, 1960 -> 2757537, 1970 -> 2825368, 1980 -> 2913808, 1990 -> 2776755, 2000 -> 2931923}, "Missouri" -> { 1790 -> 0, 1800 -> 0, 1810 -> 19783, 1820 -> 66586, 1830 -> 140455, 1840 -> 383702, 1850 -> 682044, 1860 -> 1182012, 1870 -> 1721295, 1880 -> 2168380, 1890 -> 2679185, 1900 -> 3106665, 1910 -> 3293335, 1920 -> 3404055, 1930 -> 3629367, 1940 -> 3784664, 1950 -> 3954653, 1960 -> 4319813, 1970 -> 4677623, 1980 -> 4916766, 1990 -> 5117073, 2000 -> 5606260}, "North Dakota" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 2405, 1880 -> 36909, 1890 -> 190983, 1900 -> 319146, 1910 -> 577056, 1920 -> 646872, 1930 -> 680845, 1940 -> 641935, 1950 -> 619636, 1960 -> 632446, 1970 -> 617792, 1980 -> 652717, 1990 -> 638800, 2000 -> 643756}, "South Dakota" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 4837, 1870 -> 11776, 1880 -> 98268, 1890 -> 348600, 1900 -> 401570, 1910 -> 583888, 1920 -> 636547, 1930 -> 692849, 1940 -> 642961, 1950 -> 652740, 1960 -> 680514, 1970 -> 666257, 1980 -> 690768, 1990 -> 696004, 2000 -> 756874}, "Nebraska" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 28841, 1870 -> 122993, 1880 -> 452402, 1890 -> 1062656, 1900 -> 1066300, 1910 -> 1192214, 1920 -> 1296372, 1930 -> 1377963, 1940 -> 1315834, 1950 -> 1325510, 1960 -> 1411330, 1970 -> 1485333, 1980 -> 1569825, 1990 -> 1578385, 2000 -> 1715369}, "Kansas" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 107206, 1870 -> 364399, 1880 -> 996096, 1890 -> 1428108, 1900 -> 1470495, 1910 -> 1690949, 1920 -> 1769257, 1930 -> 1880999, 1940 -> 1801028, 1950 -> 1905299, 1960 -> 2178611, 1970 -> 2249071, 1980 -> 2364236, 1990 -> 2477574, 2000 -> 2693824}, "Delaware" -> { 1790 -> 59096, 1800 -> 64273, 1810 -> 72674, 1820 -> 72749, 1830 -> 76748, 1840 -> 78085, 1850 -> 91532, 1860 -> 112216, 1870 -> 125015, 1880 -> 146608, 1890 -> 168493, 1900 -> 184735, 1910 -> 202322, 1920 -> 223003, 1930 -> 230380, 1940 -> 266505, 1950 -> 318085, 1960 -> 446292, 1970 -> 548104, 1980 -> 594338, 1990 -> 666168, 2000 -> 785068}, "Maryland" -> { 1790 -> 319728, 1800 -> 341548, 1810 -> 380546, 1820 -> 407350, 1830 -> 447040, 1840 -> 470019, 1850 -> 583034, 1860 -> 687049, 1870 -> 780894, 1880 -> 934943, 1890 -> 1042390, 1900 -> 1188044, 1910 -> 1295346, 1920 -> 1499661, 1930 -> 1631526, 1940 -> 1821244, 1950 -> 2343001, 1960 -> 3100689, 1970 -> 3923897, 1980 -> 4216933, 1990 -> 4781468, 2000 -> 5307886}, "Virginia" -> { 1790 -> 691737, 1800 -> 807557, 1810 -> 877683, 1820 -> 938261, 1830 -> 1044054, 1840 -> 1025227, 1850 -> 1119348, 1860 -> 1219630, 1870 -> 1225163, 1880 -> 1512565, 1890 -> 1655980, 1900 -> 1854184, 1910 -> 2061612, 1920 -> 2309187, 1930 -> 2421851, 1940 -> 2677773, 1950 -> 3318680, 1960 -> 3966949, 1970 -> 4651448, 1980 -> 5346797, 1990 -> 6187358, 2000 -> 7100702}, "West Virginia" -> { 1790 -> 55873, 1800 -> 78592, 1810 -> 105469, 1820 -> 136808, 1830 -> 176924, 1840 -> 224537, 1850 -> 302313, 1860 -> 376688, 1870 -> 442014, 1880 -> 618457, 1890 -> 762794, 1900 -> 958800, 1910 -> 1221119, 1920 -> 1463701, 1930 -> 1729205, 1940 -> 1901974, 1950 -> 2005552, 1960 -> 1860421, 1970 -> 1744237, 1980 -> 1950186, 1990 -> 1793477, 2000 -> 1813077}, "North Carolina" -> { 1790 -> 393751, 1800 -> 478103, 1810 -> 555500, 1820 -> 638829, 1830 -> 737987, 1840 -> 753419, 1850 -> 869039, 1860 -> 992622, 1870 -> 1071361, 1880 -> 1399750, 1890 -> 1617949, 1900 -> 1893810, 1910 -> 2206287, 1920 -> 2559123, 1930 -> 3170276, 1940 -> 3571623, 1950 -> 4061929, 1960 -> 4556155, 1970 -> 5084411, 1980 -> 5880095, 1990 -> 6628637, 2000 -> 8067673}, "South Carolina" -> { 1790 -> 249073, 1800 -> 345591, 1810 -> 415115, 1820 -> 502741, 1830 -> 581185, 1840 -> 594398, 1850 -> 668507, 1860 -> 703708, 1870 -> 705606, 1880 -> 995577, 1890 -> 1151149, 1900 -> 1340316, 1910 -> 1515400, 1920 -> 1683724, 1930 -> 1738765, 1940 -> 1899804, 1950 -> 2117027, 1960 -> 2382594, 1970 -> 2590713, 1980 -> 3120729, 1990 -> 3486703, 2000 -> 4025061}, "Georgia" -> { 1790 -> 82548, 1800 -> 162686, 1810 -> 252433, 1820 -> 340989, 1830 -> 516823, 1840 -> 691392, 1850 -> 906185, 1860 -> 1057286, 1870 -> 1184109, 1880 -> 1542180, 1890 -> 1837353, 1900 -> 2216331, 1910 -> 2609121, 1920 -> 2895832, 1930 -> 2908506, 1940 -> 3123723, 1950 -> 3444578, 1960 -> 3943116, 1970 -> 4587930, 1980 -> 5462982, 1990 -> 6478216, 2000 -> 8206975}, "Florida" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 34730, 1840 -> 54477, 1850 -> 87445, 1860 -> 140424, 1870 -> 187748, 1880 -> 269493, 1890 -> 391422, 1900 -> 528542, 1910 -> 752619, 1920 -> 968470, 1930 -> 1468211, 1940 -> 1897414, 1950 -> 2771305, 1960 -> 4951560, 1970 -> 6791418, 1980 -> 9746961, 1990 -> 12937926, 2000 -> 16028890}, "Kentucky" -> { 1790 -> 73677, 1800 -> 220955, 1810 -> 406511, 1820 -> 564317, 1830 -> 687917, 1840 -> 779828, 1850 -> 982405, 1860 -> 1155684, 1870 -> 1321011, 1880 -> 1648690, 1890 -> 1858635, 1900 -> 2147174, 1910 -> 2289905, 1920 -> 2416630, 1930 -> 2614589, 1940 -> 2845627, 1950 -> 2944806, 1960 -> 3038156, 1970 -> 3220711, 1980 -> 3660324, 1990 -> 3685296, 2000 -> 4049431}, "Tennessee" -> { 1790 -> 35691, 1800 -> 105602, 1810 -> 261727, 1820 -> 422823, 1830 -> 681904, 1840 -> 829210, 1850 -> 1002717, 1860 -> 1109801, 1870 -> 1258520, 1880 -> 1542359, 1890 -> 1767518, 1900 -> 2020616, 1910 -> 2184789, 1920 -> 2337885, 1930 -> 2616556, 1940 -> 2915841, 1950 -> 3291718, 1960 -> 3567089, 1970 -> 3926018, 1980 -> 4591023, 1990 -> 4877185, 2000 -> 5700037}, "Alabama" -> { 1790 -> 0, 1800 -> 1250, 1810 -> 9046, 1820 -> 127901, 1830 -> 309527, 1840 -> 590756, 1850 -> 771623, 1860 -> 964201, 1870 -> 996992, 1880 -> 1262505, 1890 -> 1513401, 1900 -> 1828697, 1910 -> 2138093, 1920 -> 2348174, 1930 -> 2646248, 1940 -> 2832961, 1950 -> 3061743, 1960 -> 3266740, 1970 -> 3444354, 1980 -> 3894025, 1990 -> 4040587, 2000 -> 4461130}, "Mississippi" -> { 1790 -> 0, 1800 -> 7600, 1810 -> 31306, 1820 -> 75448, 1830 -> 136621, 1840 -> 375651, 1850 -> 606526, 1860 -> 791305, 1870 -> 827922, 1880 -> 1131597, 1890 -> 1289600, 1900 -> 1551270, 1910 -> 1797114, 1920 -> 1790618, 1930 -> 2009821, 1940 -> 2183796, 1950 -> 2178914, 1960 -> 2178141, 1970 -> 2216994, 1980 -> 2520770, 1990 -> 2573216, 2000 -> 2852927}, "Arkansas" -> { 1790 -> 0, 1800 -> 0, 1810 -> 1062, 1820 -> 14273, 1830 -> 30388, 1840 -> 97574, 1850 -> 209897, 1860 -> 435450, 1870 -> 484471, 1880 -> 802525, 1890 -> 1128211, 1900 -> 1311564, 1910 -> 1574449, 1920 -> 1752204, 1930 -> 1854482, 1940 -> 1949387, 1950 -> 1909511, 1960 -> 1786272, 1970 -> 1923322, 1980 -> 2286357, 1990 -> 2350725, 2000 -> 2679733}, "Louisiana" -> { 1790 -> 0, 1800 -> 0, 1810 -> 76556, 1820 -> 153407, 1830 -> 215739, 1840 -> 352411, 1850 -> 517762, 1860 -> 708002, 1870 -> 726915, 1880 -> 939946, 1890 -> 1118588, 1900 -> 1381625, 1910 -> 1656388, 1920 -> 1798509, 1930 -> 2101593, 1940 -> 2363880, 1950 -> 2683516, 1960 -> 3257022, 1970 -> 3644637, 1980 -> 4206116, 1990 -> 4219973, 2000 -> 4480271}, "Oklahoma" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 0, 1880 -> 0, 1890 -> 258657, 1900 -> 790391, 1910 -> 1657155, 1920 -> 2028283, 1930 -> 2396040, 1940 -> 2336434, 1950 -> 2233351, 1960 -> 2328284, 1970 -> 2559463, 1980 -> 3025487, 1990 -> 3145585, 2000 -> 3458819}, "Texas" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 212592, 1860 -> 604215, 1870 -> 818579, 1880 -> 1591749, 1890 -> 2235527, 1900 -> 3048710, 1910 -> 3896542, 1920 -> 4663228, 1930 -> 5824715, 1940 -> 6414824, 1950 -> 7711194, 1960 -> 9579677, 1970 -> 11198655, 1980 -> 14225513, 1990 -> 16986510, 2000 -> 20903994}, "Montana" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 20595, 1880 -> 39159, 1890 -> 142924, 1900 -> 243329, 1910 -> 376053, 1920 -> 548889, 1930 -> 537606, 1940 -> 559456, 1950 -> 591024, 1960 -> 674767, 1970 -> 694409, 1980 -> 786690, 1990 -> 799065, 2000 -> 905316}, "Idaho" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 14999, 1880 -> 32610, 1890 -> 88548, 1900 -> 161772, 1910 -> 325594, 1920 -> 431866, 1930 -> 445032, 1940 -> 524873, 1950 -> 588637, 1960 -> 667191, 1970 -> 713015, 1980 -> 944127, 1990 -> 1006749, 2000 -> 1297274}, "Wyoming" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 9118, 1880 -> 20789, 1890 -> 62555, 1900 -> 92531, 1910 -> 145965, 1920 -> 194402, 1930 -> 225565, 1940 -> 250742, 1950 -> 290529, 1960 -> 330066, 1970 -> 332416, 1980 -> 469557, 1990 -> 453588, 2000 -> 495304}, "Colorado" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 34277, 1870 -> 39864, 1880 -> 194327, 1890 -> 413249, 1900 -> 539700, 1910 -> 799024, 1920 -> 939629, 1930 -> 1035791, 1940 -> 1123296, 1950 -> 1325089, 1960 -> 1753947, 1970 -> 2209596, 1980 -> 2889735, 1990 -> 3294394, 2000 -> 4311882}, "New Mexico" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 61547, 1860 -> 93516, 1870 -> 91874, 1880 -> 119565, 1890 -> 160282, 1900 -> 195310, 1910 -> 327301, 1920 -> 360350, 1930 -> 423317, 1940 -> 531818, 1950 -> 681187, 1960 -> 951023, 1970 -> 1017055, 1980 -> 1303302, 1990 -> 1515069, 2000 -> 1823821}, "Arizona" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 9658, 1880 -> 40440, 1890 -> 88243, 1900 -> 122931, 1910 -> 204354, 1920 -> 334162, 1930 -> 435573, 1940 -> 499261, 1950 -> 749587, 1960 -> 1302161, 1970 -> 1775399, 1980 -> 2716546, 1990 -> 3665228, 2000 -> 5140683}, "Utah" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 11380, 1860 -> 40273, 1870 -> 86786, 1880 -> 143963, 1890 -> 210779, 1900 -> 276749, 1910 -> 373351, 1920 -> 449396, 1930 -> 507847, 1940 -> 550310, 1950 -> 688862, 1960 -> 890627, 1970 -> 1059273, 1980 -> 1461037, 1990 -> 1722850, 2000 -> 2236714}, "Nevada" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 6857, 1870 -> 42491, 1880 -> 62266, 1890 -> 47355, 1900 -> 42335, 1910 -> 81875, 1920 -> 77407, 1930 -> 91058, 1940 -> 110247, 1950 -> 160083, 1960 -> 285278, 1970 -> 488738, 1980 -> 800508, 1990 -> 1201833, 2000 -> 2002032}, "Washington" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 1201, 1860 -> 11594, 1870 -> 23955, 1880 -> 75116, 1890 -> 357232, 1900 -> 518103, 1910 -> 1141990, 1920 -> 1356621, 1930 -> 1563396, 1940 -> 1736191, 1950 -> 2378963, 1960 -> 2853214, 1970 -> 3413244, 1980 -> 4132353, 1990 -> 4866692, 2000 -> 5908684}, "Oregon" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 12093, 1860 -> 52465, 1870 -> 90923, 1880 -> 174768, 1890 -> 317704, 1900 -> 413536, 1910 -> 672765, 1920 -> 783389, 1930 -> 953786, 1940 -> 1089684, 1950 -> 1521341, 1960 -> 1768687, 1970 -> 2091533, 1980 -> 2633156, 1990 -> 2842321, 2000 -> 3428543}, "California" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 92597, 1860 -> 379994, 1870 -> 560247, 1880 -> 864694, 1890 -> 1213398, 1900 -> 1485053, 1910 -> 2377549, 1920 -> 3426861, 1930 -> 5677251, 1940 -> 6907387, 1950 -> 10586223, 1960 -> 15717204, 1970 -> 19971069, 1980 -> 23667764, 1990 -> 29760021, 2000 -> 33930798}, "Alaska" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 0, 1880 -> 33426, 1890 -> 32052, 1900 -> 63592, 1910 -> 64356, 1920 -> 55036, 1930 -> 59278, 1940 -> 72524, 1950 -> 128643, 1960 -> 226167, 1970 -> 302853, 1980 -> 401851, 1990 -> 550043, 2000 -> 628933}, "Hawaii" -> { 1790 -> 0, 1800 -> 0, 1810 -> 0, 1820 -> 0, 1830 -> 0, 1840 -> 0, 1850 -> 0, 1860 -> 0, 1870 -> 0, 1880 -> 0, 1890 -> 0, 1900 -> 154001, 1910 -> 191874, 1920 -> 225881, 1930 -> 368300, 1940 -> 422770, 1950 -> 499794, 1960 -> 632772, 1970 -> 769913, 1980 -> 964691, 1990 -> 1108229, 2000 -> 1216642}}]; Null, $CellContext`stateList = Map[First, $CellContext`statePopulationRules]; Null}]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->400334623,ExpressionUUID->"d21bc9d9-d4ad-4ac0-bcd8-3b9e0731096f"], Cell[TextData[{ "\[OpenCurlyDoubleQuote]State Population Growth\[CloseCurlyDoubleQuote] from \ the Wolfram Demonstrations Project\n \ http://demonstrations.wolfram.com/StatePopulationGrowth/,\ncontributed by \ Seth J. Chandler, is ", ButtonBox["licensed under CC-BY-NC-SA.", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"] }], "Text", CellChangeTimes->{{3.6625591641396003`*^9, 3.6625591876887755`*^9}, { 3.662559474368509*^9, 3.6625594827617617`*^9}, {3.66256235638313*^9, 3.6625623697359896`*^9}, {3.662562435755429*^9, 3.6625624529124217`*^9}}, TextAlignment->Right,ExpressionUUID->"10450985-0d7f-4500-9112-22fc6b1add7b"], Cell["Exponential Growth", "Section", CellChangeTimes->{{3.544607893807447*^9, 3.5446078973456497`*^9}, { 3.5455174911212835`*^9, 3.545517491338296*^9}, {3.545517679417053*^9, 3.545517739434486*^9}, {3.6625622690885754`*^9, 3.6625622731152477`*^9}},ExpressionUUID->"823d6c47-852b-40f9-89cf-\ 335797b6085e"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "\n", StyleBox["Question 2:", FontVariations->{"Underline"->True}], " Exponential growth of P with respect to t may be described as P \ increasing by a constant factor (\[Times] r) while t increases by a constant \ term (\[CapitalDelta] t). Consider bacteria growth in the interactive frame \ below, where the initial population, ", Cell[BoxData[ FormBox[ SubscriptBox["P", "0"], TraditionalForm]],ExpressionUUID-> "6b02d193-d891-4d2e-b5ca-e07e5ad8dcea"], ", is 100 and the growth rate, r, is 0.25. \n\na. Click the play button \ for the time variable, t, in hours. Explain why the population growth is NOT \ linear. \n\nb. After how many hours will the number of bacteria double from \ the initial population? \n\nc. Choose any time t, t \[NotEqual] 0. Find \ P(t) for your t-value. After how many hours will the number of bacteria \ double from your P(t) value? What do you notice? \n\nd. Use the sliders to \ increase the ", Cell[BoxData[ FormBox[ SubscriptBox["P", "0"], TraditionalForm]],ExpressionUUID-> "45fe66ce-d860-45ec-be93-a43a3f48fb9c"], " and r values. Which parameter has more influence on how fast the \ population increases? Why?\n\n(", StyleBox["Calculus", FontSlant->"Italic"], ") \ne. Prove that the instantaneous rate of change of population at any \ time, t, is proportional to the population at that time, that is, ", Cell[BoxData[ FormBox[ FractionBox["dP", "dt"], TraditionalForm]],ExpressionUUID-> "118c7bfb-0293-43c9-9606-7917ad6b674e"], "= ", StyleBox["r\[CenterDot]P", FontSlant->"Italic"], ".\n\nf. Choose any time t, t \[NotEqual] 0. Compute P(t) and ", Cell[BoxData[ FormBox[ FractionBox["dP", "dt"], TraditionalForm]],ExpressionUUID-> "36168eac-2ec9-43a0-9f08-a337e818451e"], "at your t-value. \n\ng. Solve for the time when is the population is \ changing at a rate of 200 bacteria/hr." }], "Subsubtitle", CellGroupingRules->{"TitleGrouping", Inherited}, CellChangeTimes->CompressedData[" 1:eJxTTMoPSmViYGAQBmIQ/ZLxk0RlxitHn98GsiB66295RRCdZrVfC0TXfDyp B6ItSh4ZgGiWHbx2IFpuUpY9iHZfIrRooedrx8/uzitBtMG6EP4lQPrHwXYx ED3vZawUiJZ5Wa8LopliVpqC6PXOFy1BtNo0VVcQnXLQ3wNEq6ztOSTt9dpx 16KtD0D0o92ny3yB9KKd92pAtO1H9SYQHbF1TztY/Ij3ahC9ra1hO4iO8fq0 F0Sra096C6JPHGHf6gekj3x4tRdEC+zjPA2iX3yceAFEe385dB9Ef/n//BGI 7vqvyuEPpKtvBnODaLaDhwxB9IfTbPYgGgBnJZif "], FontSize->18, FontWeight->"Bold",ExpressionUUID->"16e89022-b13c-46b5-897b-3a0044a3510c"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`k$$ = 0.25, $CellContext`p0$$ = 100, $CellContext`showexact$$ = False, $CellContext`t$$ = 6.800000000000001, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`p0$$], 100, Subscript[ Style["P", Italic], 0]}, 0, 500, 1}, {{ Hold[$CellContext`k$$], 0.25, Style[" r", Italic]}, 0.05, 1}, {{ Hold[$CellContext`t$$], 0., Style[" t", Italic]}, 0, 10, 0.1}, { Hold[ Row[{ Column[{ Manipulate`Place[1], Manipulate`Place[2], Manipulate`Place[3]}], Column[{ Style[ Row[{ Style["\!\(\*FractionBox[\(dP\), \(dt\)]\)", 24], Style[" = ", Plain], "r P"}], 20, Italic, FontFamily -> "Times"], Style[ Row[{" P(t)", Style[" = ", Plain], "\!\(\*SubscriptBox[\(P\), \(0\)]\) ", $CellContext`e^ Style[" r t", 14]}], 20, Italic, FontFamily -> "Times"], "", "Play the animation for consistent time steps."}, Alignment -> Center]}]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`showexact$$], False, "show exact P"}, { True, False}}}, Typeset`size$$ = {547., {143.5, 149.5}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`p0$6744$$ = 0, $CellContext`k$6745$$ = 0, $CellContext`t$6746$$ = 0, $CellContext`showexact$6747$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`k$$ = 0.25, $CellContext`p0$$ = 100, $CellContext`showexact$$ = False, $CellContext`t$$ = 0.}, "ControllerVariables" :> { Hold[$CellContext`p0$$, $CellContext`p0$6744$$, 0], Hold[$CellContext`k$$, $CellContext`k$6745$$, 0], Hold[$CellContext`t$$, $CellContext`t$6746$$, 0], Hold[$CellContext`showexact$$, $CellContext`showexact$6747$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`pop$, $CellContext`x$, $CellContext`y$, \ $CellContext`z$}, $CellContext`pop$[ Pattern[$CellContext`t$, Blank[]]] := $CellContext`p0$$ E^($CellContext`k$$ $CellContext`t$); 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Null}; Typeset`initDone$$ = True), SynchronousInitialization->True, UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->439916790,ExpressionUUID->"3b52c2bf-f35b-42a1-b73c-0c4d50fb3f19"], Cell[TextData[{ "\[OpenCurlyDoubleQuote]Exponential Model for Population Growth\ \[CloseCurlyDoubleQuote]\n\ http://demonstrations.wolfram.com/ExponentialModelForPopulationGrowth/Wolfram \ Demonstrations Project\n by Abby Brown is ", ButtonBox["licensed under CC-BY-NC-SA.", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"] }], "Text", CellChangeTimes->{{3.6625591641396003`*^9, 3.6625591876887755`*^9}, { 3.662559474368509*^9, 3.6625594827617617`*^9}, {3.66256235638313*^9, 3.6625623697359896`*^9}}, TextAlignment->Right,ExpressionUUID->"8f6570b1-bff5-4c09-a2f9-2cab47f46190"], Cell[TextData[{ "Exponential Decay and Half-Life \n\n", StyleBox["What does \[OpenCurlyDoubleQuote]half-life\[CloseCurlyDoubleQuote] \ mean?? The ", FontSize->24], StyleBox["half-life", FontSize->24, FontVariations->{"Underline"->True}], StyleBox[" of an element is the ", FontSize->24], StyleBox["time", FontSize->24, FontVariations->{"Underline"->True}, FontColor->RGBColor[1, 0, 0]], StyleBox[" required for the element to decay to half (50%) of its original \ amount (100%)", FontSize->24, FontVariations->{"Underline"->True}], StyleBox[".", FontSize->24] }], "Section", CellGroupingRules->{"SectionGrouping", Inherited}, CellChangeTimes->{{3.5337248622547417`*^9, 3.533724961714431*^9}, { 3.533725066726437*^9, 3.5337250743468733`*^9}, 3.6628382893260384`*^9, { 3.662838532951494*^9, 3.6628385894209175`*^9}},ExpressionUUID->"169026fe-ff76-44ba-b28e-\ 9c3f8fd6873a"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "\n", StyleBox["Question 3:", FontVariations->{"Underline"->True}], " Like exponential growth, exponential decay of the amount, A, with respect \ to t may be described as A ", StyleBox["decreasing", FontVariations->{"Underline"->True}], " by a constant factor (a negative r-value) while t increases by a constant \ term (\[CapitalDelta] t). Consider the amount of carbon-14 (", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["C", "14"], ")"}], " "}], TraditionalForm]],ExpressionUUID-> "970dabca-a12c-4f1e-b68b-d4c3ff65b74a"], "as it decays in a sample from an initial amount of 10 grams in the \ interactive frame below.\n\na. As the interactive frame shows, carbon-14 \ decays to nitrogen-14 (with the emission of an electron) with a half-life of \ 5,730 years. Move the time slider to show that 5 grams of carbon-14 remain \ after 5,730 years.\n\nb. After how many years will there be 2.5 grams of \ carbon-14 remaining? How does this relate to the half-life of ", Cell[BoxData[ FormBox[ SubscriptBox["C", "14"], TraditionalForm]],ExpressionUUID-> "8f955e3a-83b9-40b1-8f93-7dd6dbdb2edc"], "?\n\nc. Use the half-life to solve for the decay constant, r. Then, write \ an exponential function using the form ", StyleBox["A(t) = C", FontFamily->"Arial", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ FormBox[ SuperscriptBox["e", "rt"], TraditionalForm]], FontFamily->"Arial", FontSize->18, FontColor->RGBColor[1, 0, 0],ExpressionUUID-> "83b7edf6-2c23-43a4-8b1e-ec40a0241a8b"], " that models this decay. \n\nd. How many grams of carbon-14 will \ remain after 5 half-lives? \n\ne. Solve for the amount of time necessary \ for 10 grams of carbon-14 to decay to 1 gram. \n\n(", StyleBox["Calculus", FontSlant->"Italic"], ") \nf. Calculate the rate of change of carbon-14 decay after 10,000 \ years.\n\ng. After how many years is the carbon-14 in this sample decaying \ at the rate of 2 grams/year?\n\nh. 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