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Question 480929: A lake is stocked with 500 fish, and the fish population P increases according to the following model P=10,000/1+19e^-t/5, t greater or equal than 0, where t in the time in months. After how many months will the population reach 2000?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! P increases according to the following model P=10,000/1+19e^-t/5, t greater or equal than 0, where t in the time in months. After how many months will the population reach 2000?
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P=10,000/1+19e^-t/5
2000 = 10000/[1 + 19e^(-t/5)]
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1/5 = 1/[1 + 19e^(-t/5)]
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Invert both sides to get:
1 + 19e^(-t/5) = 5
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e^(-t/5) = 4/19
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-t/5 = ln(4/19)
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-t = 5*-1.5581
t = 7.79 months
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Cheers,
Stan H.
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