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 3100. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP P kP1 dt 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) = (b) How long will it take for the population to increase to 1550 (half of the carrying capacity)? It will take years.

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 3100. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP P kP1 dt 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) = (b) How long will it take for the population to increase to 1550 (half of the carrying capacity)? It will take years.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 12CC: Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t)...

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