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 i = 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 i = 40 fish/year. Describe the solution. c) Graph the solution in the case that b = 60 fish/year. Describe the solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feaa0f9a2-7dca-4925-8c8b-274c71ab65f3%2F5af8a3c8-0caa-45f4-9622-c78e4ecc0c09%2Fvym292_processed.png&w=3840&q=75)
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.
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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