Constructing Nonlinear Models Lesson 5.7

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

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 Framulators

Exponential Model Data Matrix Plot Regression Results

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 Telecommuters

Logarithmic Model Plot Regression

Logistic Model Consider tree growth recorded Note the S shaped curve Year Height This suggests a logistic model

Logistic Model Results of Regression

Assignment Lesson 5.7 Page 466 Exercises 1 – 23 odd