Question 447946: The population of a city is growing exponentially. Initially the population was 43,000 while 7 years later the population was 79,700. Find
the population 4 years later (11 years from the beginning)
and the doubling time.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The population of a city is growing exponentially. Initially the population was 43,000 while 7 years later the population was 79,700.
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Find the population 4 years later (11 years from the beginning)
and the doubling time.
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p = ab^t
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Solve for a and b:
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Initial conditions (0,43000) so a = 43000
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p(7) = 43000*b^7 = 79,700
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Divide by 43000 and solve for "b":
b^7 = 1.8535
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b = 1.0922
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p(t) = 43000*(1.0922)^t
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Find the population 4 years later (11 years from the beginning)
p(11) = 43000*(1.0922)^11 = 113,395.39
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and the doubling time.
Solve 1.0922^t = 2
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t*log(1.0922) = log(2)
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t = 7.86 years
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Cheers,
Stan H.
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