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?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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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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