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Section 10.4:
Exponential Growth and Decay
Exponential growth and decay problems are problems involving:
Population growth
Radioactive decay
Continuous compounding of interest (money in an account in
which the compounding is continuous)
Exponential growth and decay problems are governed by the equation
A
=
A
0
e
kt
where,
A
0
=
initial quantity
A
=
final quantity
t
=
time
k
=
constant which is unique to the problem (For continuous compounding of
interest problems,
k
is the interest rate expressed as a decimal.)
Note that:
k
0
is for exponential growth, and
k
<
0
is for exponential decay.
Problem.
Carbon 14, with a halflife of 5700 years, is used to estimate the age of
organic materials.
What fraction of the original amount of carbon 14 would an object
have if it were 2000 years old?
Solution.
A
=
A
0
e
kt
Step 1 – determine
k
from halflife information.
1
2
A
0
=
A
0
e
k
5700
(
29
1
2
=
e
5700
k
ln
1
2
=
ln
e
5700
k
=
5700
k
k
=
ln
1
2
5700
=
ln1

ln 2
5700
=
0

ln2
5700
= 
ln 2
5700
Step 2 – determine the fraction of the original amount of carbon 14
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 Fall '07
 FAMIGLIETTI
 Math

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