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Question 1082600: `Can someone please help me solve this problem: In 2000 the population of a town was 35000. In 2010 it was 50000. Find an exponential model of the form f(t)=A base 0 e^kt for this population, where t is time in years since 2000. I also need help finding K but I think you have to use Ln logarithm but I am not sure.
B) what year would the population reach 100,000?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The exponential growth/decay model is
:
A = A(o) * e^kt, where A(o) is the amount we start with, k is the constant of growth or decay, t is time
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A) 50000 = 35000 * e^10k
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e^10k = 50000 / 35000 = 1.4286
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10k = ln 1.4286 = 0.3567
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k = 0.3567 / 10 = 0.03567
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B) 100000 = 35000 * e^(0.03567t)
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e^(0.03567t) = 100000 / 35000 = 2.8571
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0.03567t = ln 2.8571 = 1.0498
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t = 1.0498 / 0.03567 = 29.4309 approx 29
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the population will be 100000 in year 2029
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