Students can do a lot of comparison with others to see whose prediction model was most accurate. Students can also use graphing calculators to graph the functions they created. An excellent application of exponential decay is half-life. Using random sample sizes, students can find out how much of a particular isotope remains through use of half-life information for any of the chemical elements. Students can first read about the concept of half-life and then create exponential decay models to solve given problems.
Students can also use graphing calculators to graph the situations.
When working with compound interest, the use of real-world data certainly makes things more interesting. Interest rates for banks all across the United States are available to the public. This can be used for more practice, contests, etc. Many, many applications are possible. This is a very practical lesson for students.