SOLUTION: A group of 30 fish of a certain species is released in lake.With a careful management the number of fish.N,t years is expected that N=330/{ 1+10(0.81)^T } and the fish popula

Question 1102063: A group of 30 fish of a certain species is released in lake.With a careful management the number of fish.N,t years is expected that
N=330/{ 1+10(0.81)^T }
and the fish population will be able to maintain itself without ay protection when the population reaches a size of 80.How many years must a protection program be maintained for the fish population?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
t or T ? Choose one but not both.

You basically want to solve for t. Once done, let N=80 and evaluate t.

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Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Mathematically, the question is: at which t the quantity N = 330/(1+10(0.81)^t) = will reach the value of 80. I will show the plot first Plot y = Next, I will show the table Year, t N = 330/(1+10(0.81)^t 0 30.00 1 36.26 2 43.65 3 52.26 4 62.21 5 73.55 6 86.29 From the plot and from the table you can see that the number N increases monotonically and will exceed the value of 80 in 6 years.

Answer. How many years must a protection program be maintained for the fish population?   - 6 years.

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