SOLUTION: 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.

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)]
----
1/5 = 1/[1 + 19e^(-t/5)]
---
Invert both sides to get:
1 + 19e^(-t/5) = 5
---
e^(-t/5) = 4/19
---
-t/5 = ln(4/19)
---
-t = 5*-1.5581
t = 7.79 months
=================
Cheers,
Stan H.
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