Students explore the use of exponential decay models in the context of eliminating caffeine and lead from the body. The problem starts with generalizing the relationship between time and the amount of chemical left in the body to writing an explicit rule and connecting it to the graphical representation.

Students explore the use of exponential decay models in the context of eliminating caffeine and lead from the body. The problem starts with generalizing the relationship between time and the amount of chemical left in the body to writing an explicit rule and connecting it to the graphical representation. The caffeine problem develops the concept of half-life and extends to writing a rule and graphing a piecewise function based on students’ own caffeine consumption. The lead problem also explores the concept of half-life and uses logarithms to solve exponential functions for given values of the dependent variable. Activity sheets and solutions are included. This mathematically rich problem was developed for the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools proposed by the Ohio Department of Education. (author/sw)