First, students will learn how to sketch exponential functions with base \(e,\) with and without transformations. Then students will learn how to solve word problems involving exponential growth and decay. Specifically, they'll use \(Q(t) = Q_0e^{kt}\) or \(Q_0e^{-kt},\) to solve such word problems. Here, \(Q\) is some quantity, \(t\) is time, and \(k\) is the growth or decay constant.
Conclude by giving your students these challenges:
- Augustus' Age by NRICH
- Shapely Lines by NRICH
- Two Egg Timers by NRICH
- 2006 AMC 8, Problem 5
- 2010 AMC 8, Problem 19
- 2007 AMC 8, Problem 9