Problem 10: A fish hatchery has 500 fish at t = 0, when harvesting begins at a rate of b> 0 fish/year. The fish population is modeled by the initial value problem y' (t) = 0.01 y-b, y(0) = 500, where t is measured in years. a) Find the fish population, for t≥ 0, in terms of the harvesting rate b. (i.e. find the function y[t]). y(t) = for t≥ 0. b) Graph the solution in the case that b = 40 fish/year. Describe the solution. c) Graph the solution in the case that b = 60 fish/year. Describe the solution.

Problem 10: A fish hatchery has 500 fish at t = 0, when harvesting begins at a rate of b> 0 fish/year. The fish population is modeled by the initial value problem y' (t) = 0.01 y-b, y(0) = 500, where t is measured in years. a) Find the fish population, for t≥ 0, in terms of the harvesting rate b. (i.e. find the function y[t]). y(t) = for t≥ 0. b) Graph the solution in the case that b = 40 fish/year. Describe the solution. c) Graph the solution in the case that b = 60 fish/year. Describe the solution.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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