In a traditional mathematics curriculum, middle school students' experiences with functions in algebra are usually limited to linear relationships. However, a number of realworld experiences (e.g., compound interest, population growth, and the amount of a drug remaining in a subject's bloodstream) involve exponential functions. In this article, I describe two problems involving exponential functions and some basic probability concepts that were used in an eighthgrade class, which led to greater student understanding about the general form of an exponential function. I also describe how students used graphing calculators to help them make sense of the values that are used in the general form and how they relate to the context of the problem.
Jeff Wanko is interested in number theory, geometry, puzzles, the history of mathematics, and the integration of mathematics with the arts.