## 1.7 Case Study: Modeling with Elementary Functions

### Summary

The purpose of this CSC is find a good fit of the AIDS data in order to predict the number of AIDS cases in the future.

By the time you complete the CSC, you should know:

• How to fit an exponential function to data by the method of Least Squares.
• How to determine mathematically which is the best among two or more different fitting functions.
• The kinds of considerations that go into determining the best fitting function.
• How to use your own analysis to argue a position.
• How to work with one or more other students on a team project.
• How to write a CSC report.
• An example of applying mathematics you have learned to solving a real-world problem.

### Examples

A succession of forest fires has been decimating the countryside. A table of data is available, giving the days elapsed and acres destroyed. Two functions have been suggested to model the data. Which one is a better fit?

After examining the data in the table, it is suggested that since the amount of damage is increasing so quickly, perhaps an exponential function would be a better fit. Is this true? Find the best-fit exponential function and determine if it does in fact model the data more precisely.

Use the two polynomials suggested in example 1 to predict the number of acres destroyed after 30, 40, and 50 days. It turns out that after 30 days, the number of acres destroyed was 25100. What was the percentage error in each of your estimates? How does this reflect on your choice of modeling function?

### Applets

Fitting AIDS Data

### Videos

See short videos of worked problems for this section.

### Exercises

See Exercises for 1.7 Case Study: Modeling with Elementary Functions (PDF).

Work online to solve the exercises for this section, or for any other section of the textbook.

#### Interesting Application

Mathematicians hard at work: See a
publication on jobs with the government.

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel