1.7 Case Study: Modeling with Elementary Functions



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:

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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?


Fitting AIDS Data


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Interesting Application

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

1.6 Exponential and Logarithm Functions Table of Contents 2.1 Modeling Rates of Change

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