PreCalculus: Lesson Plan * 10/31/2006

Quickstart
1. Solve for x: 7^x = 3; x ≈ 0.5646
2. Solve for x: log(x + 4) + log(x + 1) = 1; x = 1 (x = -6 is not in the domain.)

Lesson
3.5 Exponential and Logarithmic Models
Objective: Students will know how to fit exponential and logarithmic models to sets of data, and how to use exponential growth models, exponential decay models, logistic growth models, and logarithmic models to solve applications.

I. Introduction
The five most common types of mathematical models involving exponential functions and logarithmic functions are as follows.
1. Exponential growth model
2. Exponential decay model
3. Gaussian model
4. Logistic growh model
5. Logarithmic models
See p.258 for their general forms and basic shapes

Check Understanding
p.266 #1 - 14

II. Exponential Growth and Decay
Example 1: Population Growth p.259

Map of countries by population. From wikipedia.com

Example 2: Modeling Population Growth p.260
Example 3: Carbon Dating

IV. Logistic Growth Model p.263
Some populations initially have rapid growth, followed by declining rate of growth. One model for describing this type of growth pattern is the logistic curve, called a sigmoidal curve.

Example 5: Spread of a Virus p.263

V. Logarithmic Models p.264
Example 6: Magnitudes of Earthquakes

VI. Fitting Models to Data pp.264 - 265
Example 7: Fitting a Logarithmic Model
Example 8: Fitting an Exponential Model