Suppose that the differential equation dy dt (3) models a logistic equation with harvesting, where y(t) represents a spotted grunter popu- lation (Figure 1) in the Knysna Lagoon at time t, measured in years. ⒸSAIAB Write down the = y(40-y) - 300 Figure 1: The spotted grunter. (Image courtesy of: https://wwfsassi.co.za/fish-detail/44/) (a) per capita growth rate of the spotted grunter population. (b) carrying capacity of the lagoon. (c) rate at which the spotted grunter are harvested from the lagoon.
Suppose that the differential equation dy dt (3) models a logistic equation with harvesting, where y(t) represents a spotted grunter popu- lation (Figure 1) in the Knysna Lagoon at time t, measured in years. ⒸSAIAB Write down the = y(40-y) - 300 Figure 1: The spotted grunter. (Image courtesy of: https://wwfsassi.co.za/fish-detail/44/) (a) per capita growth rate of the spotted grunter population. (b) carrying capacity of the lagoon. (c) rate at which the spotted grunter are harvested from the lagoon.
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.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 2EA
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Transcribed Image Text:Suppose that the differential equation
dy
dt
(3)
models a logistic equation with harvesting, where y(t) represents a spotted grunter popu-
lation (Figure 1) in the Knysna Lagoon at time t, measured in years.
ⒸSAIAB
Write down the
= y(40-y) - 300
Figure 1: The spotted grunter. (Image courtesy of: https://wwfsassi.co.za/fish-detail/44/)
(a) per capita growth rate of the spotted grunter population.
(b) carrying capacity of the lagoon.
(c) rate at which the spotted grunter are harvested from the lagoon.
(d) Determine the
(i) critical points of Eq. (3).
(ii) limiting and threshold solutions from Eq. (3).
(iii) stability of the critical points by drawing a phase diagram for Eq. (3).
(e) (i) Taking y(0) = 11 and a step size of h = 1/12, apply four iterations of the Forward.
Euler Formula to approximate the solution of Eq. (3). Apply two decimal place rounding
where applicable.
(ii) How do your results from (e) (i) compare with what the phase diagram for Eq. (3)
reveals?
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