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Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP P(1-2), 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 3000 (half of the carrying capacity)? It will take years.

Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP P(1-2), 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 3000 (half of the carrying capacity)? It will take years.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 44E: Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program...
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Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP *P(1-P) dt k= determine the constant k, and then solve the equation to find an expression for the size of the population after t years. = P(t): = = 7 (b) How long will it take for the population to increase to 3000 (half of the carrying capacity)? It will take years.
Transcribed Image Text:Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP *P(1-P) dt k= determine the constant k, and then solve the equation to find an expression for the size of the population after t years. = P(t): = = 7 (b) How long will it take for the population to increase to 3000 (half of the carrying capacity)? It will take years.
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