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Applications of Exponential and Log Equations
Exponential and Logarithmic functions have perhaps more realworld applications than
any other class of functions at the precalculus level and beyond.
These functions
govern population increase as well as interest income in a bank.
And since (it seems)
virtually everything decays exponentially, we can apply exponential decay equations to
many different applications (see
http://www.mathmotivation.com/science/carvalue.html
)
Exponential Growth and Decline:
Exponential growth and decline is governed by the function:
N(t)
= N
o
e
kt
where
N
o
= the original amount at time t=0.
k = the (decimal) rate of growth per time period, be it years, days, etc.
t = the units used in the time period.
N(t) = the amount at time t
NOTE: N(t) means “N as a function of t”, NOT “N times t”!
Example:
A population grows exponentially 3% per year. If the population is initially
1000, how many years will it take for the population to double to 2000?
How many years
will it take for the population to reach 4000?
Since the original amount is 1000, N
o
=1000.
Also, we know that N(t) = 2000 and also
N(t) = 4000.
In both cases, k = 0.03 . So we have to solve the equations:
2000 = 1000e
0.03t
and
4000 = 1000e
0.03t
.
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 Fall '09
 Crandall
 Anthropology, Exponential Function, Logarithm, Exponential decay, Property of Equality

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