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Unformatted text preview: exponential and logarithmic functions are used to model a wide
variety of behaviors in the real world. In the examples that follow, note that while the applications
are drawn from many diﬀerent disciplines, the mathematics remains essentially the same. Due to
the applied nature of the problems we will examine in this section, the calculator is often used to
express our answers as decimal approximations. 6.5.1 Applications of Exponential Functions Perhaps the most well-known application of exponential functions comes from the ﬁnancial world.
Suppose you have $100 to invest at your local bank and they are oﬀering a whopping 5 % annual
percentage interest rate. This means that after one year, the bank will pay you 5% of that $100,
or $100(0.05) = $5 in interest, so you now have $105.1 This is in accordance with the formula
for simple interest which you have undoubtedly run across at some point in your mathematical
Equation 6.1. Simple Interest The amount of interest I accrued at an annual rate r on an
investmenta P after t years is
I = P rt
The amount A in the account after t years is given by
A = P + I = P + P rt = P (1 + rt)
a Called the principal Suppose, however, that six months into the year, you hear of a better deal at a rival bank.2
Naturally, you with...
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