Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be9300. The number of fish tripled in the first year.(a) Assuming that the size of the fish population satisfies the logistic equation(1-).dP= kPdtdetermine the constant k, and then solve the equation to find an expression for the size of the population after t years.k =P(t) =(b) How long will it take for the population to increase to 4650 (half of the carrying capacity)?It will takeyears.

Name: Biologists stocked a lake with 500 fish and estimated the carrying ca
Uploaded: 2024-03-20T07:06:41.000Z
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Description: Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be9300. The number of fish tripled in the first year.(a) Assuming that the size of the fish population

Given, Initial Population of fish = 500 The carrying capacity = 9300 Number of fish tripled in the…

Math

Calculus

Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 9300. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP *-(1-). kP dt 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) = (b) How long will it take for the population to increase to 4650 (half of the carrying capacity)? It will take years.