In this lesson, students see that for any equal intervals of input, including those for a fractional amount, the output values change by the same factor. For example, if the growth factor of a function is known for the interval from 15 minutes after an event to 45 minutes after the event, then the same growth factor applies to every 30-minute interval in which this same exponential behavior is applied.

In an optional activity, students calculate average rates of change for an exponential function. This activity is optional because it goes beyond the requirements of the standards.

Students must use the structure of exponential growth and exponential functions to recognize that all intervals of the same length are affected by the same growth factor (MP7).

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.