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Math 1314
Lesson 15
Exponential Functions as Mathematical Models
In this lesson, we will look at a few applications involving exponential functions.
We’ll first
consider some word problems having to do with money.
Next, we’ll consider exponential
growth and decay problems.
Interest Problems
From previous course work, you may have encountered the compound interest formula:
mt
m
r
P
A
+
=
1
P
= principal amount invested
A
= accumulated amount
r
= interest rate
m
= number of times interest is compounded per
year
t
= time in years
Now suppose we let the number of compounding periods increase; that is, we’ll take the limit
of this function as
m
goes to infinity:
mt
m
m
r
P
+
∞
→
1
lim
This is a fairly complicated limit to evaluate, so we will omit the details.
rt
mt
m
Pe
m
r
P
=
+
∞
→
1
lim
You may also have seen this formula before.
This is the interest formula to use when interest is
compounded continuously.
We’ll be interested in two kinds of problems, those that ask for an accumulated amount and

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