1. Constructing Nonlinear Models
Lesson 5.7

2. Modeling Data
When data are recorded from observing an experiment or phenomenon
May increase/decrease at a constant rate This would require a linear model
May increase/decrease rapidly This would signify an exponential model
May increase gradually over time Indicating a logarithmic model
May go from slow to rapid increase then level off Suggests a logistic model

3. Exponential Model
Given a table which projects the number of framulators produced during given years.
Place in data matrix
Plot
Use exponential regression to determine a modeling function
Use function to make predictions
Year
2005
2010
2015
2020
Framulators 20 41 80
136

4. Exponential Model
Data Matrix
Plot
Regression Results

5. Logarithmic Model
Consider the number of telecommuters (in millions) for years given
Gradual increase suggests logarithmic model
Place in data matrix (note, don't use year 0)
Plot
Use exponential regression to determine a modeling function
Use function to make predictions
Year 97 98 99 00 01 02 03 04 05
Telecommuters
9.2
9.6
10.0
10.4
10.6
11.0
11.1
11.2
11.3

6. Logarithmic Model
Plot
Regression

7. This suggests a logistic model
Consider tree growth recorded
Note the S shaped curve
Year 5 10 20 30 40 50
Height 3 8 32 47
49.5
59.9
This suggests a logistic model

8. Logistic Model
Results of Regression

9. Assignment
Lesson 5.7
Page 436
Exercises 1 – 17 odd