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Lecture 24: Section 3.5
Exponential and Logarithmic Models
Three common types of mathematical models involv
ing exponential functions and logarithmic functions:
1. Exponential growth model:
y
=
ae
bt
where
y
= amount at time
t
a
= amount at time 0
b
= relative growth rate,
b >
0 (in decimal)
t
= time
t
y
NOTE:
If the doubling time
T
is given, then
b
=
ln 2
T
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A certain breed of rabbit was introduced onto
a small island 8 years ago. The current rabbit pop
ulation on the island is estimated to be 4100, with a
relative growth rate of 55% per year.
1) What was the initial size of the rabbit population?
2) Estimate the population 2 years from now.
3) How long does it take the population to double?
2. Exponential decay model:
y
=
ae
±
bt
where
y
= amount at time
t
a
= amount at time 0
b
= relative decay rate,
b >
0
t
= time
t
y
NOTE:
If the half life
T
is given, then
b
=
ln 2
T
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A radioactive material decays according to the
model
y
=
ae
±
0
:
0244
t
. Assume that a scientist has a
sample of 500 grams of it.
1) What is its decay rate?
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This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.
 Spring '08
 WILLIAMSON
 Calculus, Algebra

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