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The growth of a certain population (in millions) over time, P(t), is modelled by the differential equation P': = 6P - P² - h. The parameter h in the equation is the harvesting rate (in millions per year). (a) Determine if the population will grow, be steady, or decline in the following cases i) h=5, P(0) = 1, ii) h=5, P(0) = 5, iii) h=10, P(0) = 5. (b) What should the harvest rate be if we want P = 4 to be an equilibrium population? (c) For what values of the harvest rate, h, does a stable equilibrium population exist?

The growth of a certain population (in millions) over time, P(t), is modelled by the differential equation P': = 6P - P² - h. The parameter h in the equation is the harvesting rate (in millions per year). (a) Determine if the population will grow, be steady, or decline in the following cases i) h=5, P(0) = 1, ii) h=5, P(0) = 5, iii) h=10, P(0) = 5. (b) What should the harvest rate be if we want P = 4 to be an equilibrium population? (c) For what values of the harvest rate, h, does a stable equilibrium population exist?

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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The growth of a certain population (in millions) over time, P(t), is modelled by the differential equation P' = 6P P² - h. The parameter h in the equation is the harvesting rate (in millions per year). (a) Determine if the population will grow, be steady, or decline in the following cases i) h=5, P(0) = 1, ii) h=5, P(0) = 5, iii) h=10, P(0) = 5. (b) What should the harvest rate be if we want P = 4 to be an equilibrium population? (c) For what values of the harvest rate, h, does a stable equilibrium population exist?
Transcribed Image Text:The growth of a certain population (in millions) over time, P(t), is modelled by the differential equation P' = 6P P² - h. The parameter h in the equation is the harvesting rate (in millions per year). (a) Determine if the population will grow, be steady, or decline in the following cases i) h=5, P(0) = 1, ii) h=5, P(0) = 5, iii) h=10, P(0) = 5. (b) What should the harvest rate be if we want P = 4 to be an equilibrium population? (c) For what values of the harvest rate, h, does a stable equilibrium population exist?
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