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In this lecture we consider an extended application of the ideas of the first four lectures, namely, modeling AIDS data.
Quick Question
How many solutions does the equation e^{x} − x^{2} − 1 = 0 have?
Answer
Outline
Outline for Case Study: Modeling with Elementary Functions
Textbook
Sec. 1.7, Case Study: Modeling with Elementary Functions
Today's Homework
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Quiz
Case Study: Modeling with Elementary Functions Quiz
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 bestfit 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

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

Sum of Squared Errors and Comparing Two Lines
