Find the limit. (If an answer does not exist, enter DNE.) Biologists stocked a l

Question

Find the limit. (If an answer does not exist, enter DNE.)

Biologists stocked a lake with 156 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 9500. The number of fish doubled in the first year. Assuming that the size of the fish population satisfies the logistic equation dP/dt = kP(1 - P/k), determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k = P(t) = How long will it take for the population to increase to 4750 (half of the carrying capacity)? It will take years

Explanation / Answer

taking 64 x^2 out of the root taking common cancels out with the denominator and inside the root the leftover is 1+1/64x

which gives 1 for x -> infinity

so the answer is 1 for this limit

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