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 Year2005201020152020 Framulators204180136

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 Year979899000102030405 Telecommuters9.29.610.010.410.611.011.111.211.3

6. Logarithmic Model Plot Regression

7. Logistic Model Consider tree growth recorded Note the S shaped curve Year51020304050 Height38324749.559.9 This suggests a logistic model

8. Logistic Model Results of Regression

9. Assignment Lesson 5.7 Page 466 Exercises 1 – 23 odd