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Applications of Exponential Functions - Growth & Decay
• There are many applications of exponential functions
in the areas of growth and decay.
Growth Model
kt
A( t )  A 0 e , k  0
Decay Model
kt
A( t )  A 0 e , k  0
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Applications of Exponential Functions - Growth & Decay
• Example 1:
Consider the model A( t )  A 0 e  0.000121t
representing the amount of decay of carbon-14, where ...
t = time in years
A0 = initial amount of carbon-14
A(t) = amount of carbon-14 after t years
Assume that a bone originally had 20 grams of
carbon-14 present. How many grams will be present
1000 years later?
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Applications of Exponential Functions - Growth & Decay
• Letting A0 = 20 and t = 1000 yields ...
A(1000)  20e
(  0.000121)(1000)
... or approximately 17.72 grams of carbon-14 remaining.
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Applications of Exponential Functions - Growth & Decay
• Example 2:
60,000
Consider the model N( t ) 
2 t
1  400e
where ...
t = time in weeks
N(t) = is the number of people who have the flu in a
certain state t weeks after the initial outbreak.
Find the following:
a) the number of people ill with the flu when the
epidemic began.
b) the number of people ill with the flu after 3 weeks.
c) the total number of people with the flu at the end of
the epidemic.
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Applications of Exponential Functions - Growth & Decay
• The most efficient way to answer the questions would
be to use the TABLE feature on a graphing calculator.
Type in the formula into y1,
60,000
set TBLSET to 0, 1, auto,
N( t ) 
2 t
1  400e
and then go to TABLE.
a) Letting t = 0 represent the
beginning of the epidemic,
there were approximately
150 people ill with the flu
initially.
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Applications of Exponential Functions - Growth & Decay
b) A value of t = 3 represents the number of people ill
after 3 weeks, or approximately 30,128 people.
c) To find the total number of people with the flu at the
end of the epidemic, consider what value N(t) is
approaching as the value of t
increases. Scrolling down
in the table yields ...
which suggests 60,000
people.
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Applications of Exponential Functions - Growth & Decay
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