Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6300. The number of fish doubled in the first year. (a) 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. (b) How long will it take for the population to increase to 3150 (half of the carrying capacity)?

Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6300. The number of fish doubled in the first year. (a) 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. (b) How long will it take for the population to increase to 3150 (half of the carrying capacity)?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 15T

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