In this lesson, students recall geometric sequences as a reintroduction of exponential functions from a previous course. Some features of exponential change are featured, such as change by a constant growth factor multiple, the relationship between the growth factor and whether the function grows or decays, and that exponential growth happens slowly at first, then rapidly later.

Students must consider inputs that are not whole numbers and the meaning of negative time values in context.

Students must reason abstractly and quantitatively (MP2) when they express situations in different representations, such as verbal descriptions and graphs. They may also use repeated reasoning (MP8) to draw the connection between geometric sequences and exponential growth.

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