In this lesson, students encounter exponential functions of the form  and use tables and graphs to compare them to exponential functions of the form or .

Although it is beyond the scope of this course to go into the details, they learn that the form with base is often used to model situations where the growth rate  happens continuously—not just for each unit of time but at every moment.

Next, after experimenting with some concrete representations of functions written with base , students interpret and analyze the parameters of such equations more formally. They reason abstractly and quantitatively about the meaning of various quantities in context (MP2).

The lesson includes an optional activity for students to practice graphing functions expressed with base and adjusting the graphing window so that the graphs are useful for analysis and problem solving.