The purpose of this lesson is for students to revisit the idea of average rate of change and apply it to exponential functions. While rate of change has an unambiguous meaning for linear functions, for nonlinear functions rates of change are not constant, so an interval must be specified.

In this lesson, students first are invited to recall how to calculate an average rate of change for a specific interval for a function represented by a data table. By comparing the average rate of change of different intervals that all start at the same point, students can observe that while the average rate of change can describe how the data is changing with reasonable accuracy over some intervals, it is not a good predictor over larger intervals, because exponential functions do not have a constant rate of change. Contexts are used throughout this lesson to give students an opportunity to reason abstractly and quantitatively (MP2).