In this lesson we will consider exponential growth problems. Exponential growth occurs when some quantity regularly increases by a fixed percentage. Examples of exponential growth include
We will study the phenomenon of exponential growth by beginning with the economic model of annual interest. We will then look at what happens when annual interest is compounded more frequently. This will lead us naturally into the realities of exponential growth in nature, where increases are continuous rather than discrete.
The ideas that we will study can be applied to a broad spectrum of problems, some of which you will investigate in the exercises. Along the way, we will use Maple to motivate and illustrate the idea of user-defined functions.