1.7 Case Study: Modeling with Elementary Functions
By the time you complete the CSC, you should know:
On-screen applet instructions: Click here for further instructions.
ExamplesA 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?
AppletsFitting AIDS Data
VideosSee short videos of worked problems for this section.
ExercisesSee 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.
Resources on the WebInformation on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
|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