2. CHAPTER 5 LESSON 4 Exponential and Logarithmic Models

3. Finding Exponential Model

4. Insurance Premiums The monthly premiums for $250,000 in term-life insurance over a 10-year term period increase with the age of the men purchasing the insurance. The monthly premiums for nonsmoking males in shown. Graph the data in the table with x as age and y in dollars. Create an exponential function that models these premiums as a function of age. Graph the data and the exponential function that models the data on the same axes. Age (years)Monthly Premium (dollars) 35123 40148 45225 50338 55500 60783 651330 702448 754400

5. Smokers The percent's of U.S. males 18 years of age or older who smoked in selected years from 1965 to 2004 are given in the table. Graph the data, with x equal to the number of years after 1960 Find an exponential function that models the data, using as input the number of years after 1960 Graph the data and the exponential function that models the data on the same axes. Use the model to estimate the percent of U.S. male smokers age 18 and over in 2008. YearPercent 196551.6 197442.9 197937.2 198334.7 198532.1 198731.0 199028.0 199127.5 199228.2 199327.5 199427.8 199526.7 200025.7 200225.2 200324.1 200423.4

6. Constant Percent Changes If the percent change of the outputs of a set of data is constant for equally spaced inputs, an exponential function will be a perfect fit for the data If the percent change of the outputs is approximately constant for equally spaced inputs, an exponential function will be an approximate fit for the data

7. Constant Percent Changes X0123456789 Y1248163264128256512

8. Sales Decay Suppose a company develops a product that is released with great expectations and extensive advertising, but sales suffer due to bad word of mouth from dissatisfied customers. Use the monthly sales data below to determine the percent change for each of the months given. Find the exponential function that models the data. Graph the data and the model on the same axes. Month12345678 Sales ($ thousands)780608475370289225176137

9. Exponential Model

10. Inflation

11. Technology Note When using technology to fit an exponential model to data, you should align the inputs to reasonably small values

12. Finding a Logarithmic Model Follow same steps as finding exponential model Select option 9: LnReg instead of option 0:ExpReg

13. Mothers in the Workforce The table gives the percent of mothers who returned to the workforce within 1 year after having a child (for the years 1976-2004). Find a logarithmic model for this data, with x equal to the number of years after 1970. YearReturning Mothers (%) 197631 197836 198039 198243 198448 198650 198851 199052 199253 199452 199555 199859 200055 200455

14. Technology Note When using technology to fit a logarithmic model to data, you must align the data so that all input values are positive.

15. Female Workers The percent of all workers who are female during selected years from 1970 to 2006 is given in the table. Find a logarithmic function that models this data. Align the input to be the number of years after 1960. Graph the equation and the aligned data points. Comment on how the model fits the data. Assuming that the model is valid in 2010, use it to estimate the percent of female workers in 2010. Year% 197030.0 197531.9 198035.3 198537.9 199037.2 199540.3 200041.2 200541.3 200641.5

16. Reminder on Models

17. Homework Pages 373-378 1-4,7-10,13,15,16,18,20,21,23,25,27,31,32