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
- bank accounts on which fixed interest is accumulating,
- human populations unhindered by predation or environmental problems, and
- contagious diseases for which no immunization is available.
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
Joseph L. Zachary
Department of Computer Science
University of Utah