In this lesson, students analyze the graph of an exponential function  given by . In particular, they study the effect of on the shape of the graph. To observe how affects the shape of the graph when and when , they simultaneously examine several functions of this form, all of which have the same value of .

Narrow contexts are used in these lessons to encourage greater attention to the growth factors of the different functions, rather than on interpreting the quantities in context. Since students are focusing mainly on understanding how varying  affects the graph, they are looking at the structure of an exponential function and its graph (MP7).

One of the activities in this lesson works best when each student has access to devices that can run a Desmos applet because students will benefit from seeing the relationship in a dynamic way.