1. 1 6.9 Exponential, Logarithmic & Logistic Models In this section, we will study the following topics: Classifying scatter plots Using the graphing calculator to find models for data Fitting exponential, logarithmic, and logistic models to data

2. 2 Classifying Scatter Plots Example: Decide whether the scatter plot could best be modeled by a linear, quadratic, exponential, logarithmic, or logistic model. I II III IV V

3. 3 Fitting Exponential, Logarithmic, and Logistic Models to Data To find an exponential, logarithmic, or logistic model for a set of data using the TI-83 graphing calculator, follow the same steps you have used for linear and quadratic regression. After you have entered your data into lists and viewed your stat plot, go to  CALC and choose one of the following: 9: LnReg for a natural logarithmic model 0: ExpReg for an exponential model B: Logistic for a logistic model

4. 4 Here’s what you will see: 9: LnReg for a natural logarithmic model 0: ExpReg for an exponential model B: Logistic for a logistic model

5. 5 The number of Starbucks stores substantially increased between 1987 and 2001. YearNumber of Stores 198717 198955 1991116 1993272 1995676 19971412 19992135 20014709 Example

6. 6 Let f(t) represent the number of stores at t years since 1980. 1. Enter data, graph scatter plot, and determine appropriate model. 2. Find the regression equation for the data. Round values to three decimal places. 3. What is the percent rate of growth of stores during this period (1987 – 2001)?

7. 7 4. What does the coefficient “a” represent within the context of this problem? 5. If the number of stores was to continue at the same rate, predict the number of stores in 2008. Do you think that this is a good model for predicting the number of stores in 2008? Explain.

8. 8 More Examples Pp 492-93 #5, 7, 9

9. 9 End of Section 6.9