A great example to use for exponential growth is population. Since population generally grows exponentially, students can use population data to create an exponential growth model and predict future populations. The population of the United States from 1790-1990 is a good source of data for creating an exponential growth function. If you'd like to see population data for the world other countries , that is available from the Census also. 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.