Topic 1: Exponential and Logarithmic Functions

• • Review of Exponential Functions
  • Review of Logarithmic Functions

Topic 2: Derivatives of Exponential (base e) Functions

• • Derivatives with e – The main idea
  • Derivatives of Exponential Functions (lecture)
  • Application Problem:  A Logistic Function

(MTH 263 only)

• • Chain Rule Twice with e and Sine Functions
  • Chain Rule Twice to Find y’ and y”
  • Hyperbolic Functions – The Main Idea
  • Hyperbolic Identities and Derivatives

Topic 3: Derivatives of Natural Logarithmic Functions

• • Derivatives of log functions – The main idea
  • The Derivative of the Natural Log Function

(MTH 263 only)

• • Logarithmic Differentiation Example

Topic 4: Uninhibited and Limited Growth Models (Section 2.4)

• • Uninhibited Growth Models – The Main Idea (lecture)
  • Uninhibited Growth Model – Wind Energy Problem
  • Logistic Growth Example – SARS
  • Logistic Growth Example – COVID
  • Learning Curve Example

Topic 5: Exponential Decay

• • Exponential Decay (lecture)
  • The Decay of a Plastic Bottle (example)
  • Newton’s Law of Cooling (example)

Topic 6: The Derivatives of and b^x and log_bx

• • Derivatives of Exponentials and Logs of Base b – The Main Idea (lecture)
  • Application Problems – Depreciation and Decay

Interactive CDF file: (the free CDF Player is required to view these files)

Exponential Growth and Decay

The Logistic Function – SARS example