SOLUTION: The population of a small suburban town grows exponentially and was 12 000 in 1993 and 21 000 in 1998. In what year will the population reach 36 750?

Question 688126: The population of a small suburban town grows exponentially and was 12 000 in 1993 and 21 000 in 1998. In what year will the population reach 36 750?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The population of a small suburban town grows exponentially and was 12 000 in 1993 and 21 000 in 1998. In what year will the population reach 36 750?
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Form : A(t) = ab^t where t is # of years after 1993.
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Solve for "a" and "b" using (0,12000) and (5,21000).
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Using 0,12000 you get: 12000 = ab^0
So a = 12000
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Equation:
A(t) = 12000*b^t
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Using (5,21000), solve for "b":
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21000 = 12000*b^5
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b^5 = 21/12 = 7/4
b = (7/4)^(1/5)
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Equation:
A(t) = 12000*(7/4)^(t/5)
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In what year will the population reach 36 750?
Solve:
36750 = 12000(7/4)^(t/5)
(7/4)^(t/5) = 3.0625
Take the log to solve for "t":
(t/5)log(7/4) = log(3.0625)
(t/5) = log(3.0625)/log(7/4)
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t = 1.68 years
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Cheers,
Stan H.
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