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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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.
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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.
Transcribed Image Text: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.
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