This lesson revisits the fact that exponential functions grow more quickly, eventually, than do linear functions. The first activity compares simple interest (linear growth) with compound interest (exponential growth). Students examine tables and graphs and see that the exponential function quickly overtakes the linear function. In the second activity, the exponential function is deliberately chosen to grow slowly over a large domain, making it less clear whether or not the exponential function will overtake the linear function.

The second activity provides an opportunity for students to strategically use technology (MP5), whether they make a graph (for which they will need to think carefully about the domain and range) or continue to tabulate explicit values of the two functions (likely with the aid of a calculator for the exponential function). This lesson provides multiple opportunities for students to justify their reasoning and critique the reasoning of others (MP3).