Please help with D and E (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 ForwardEuler Formula to approximate the solution of Eq. (3). Apply two decimal place roundingwhere applicable.(ii) How do your results from (e) (i) compare with what the phase diagram for Eq. (3)reveals? Suppose that the differential equationdydt= y(40-y) - 300models 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.ⒸSAIABFigure 1: The spotted grunter. (Image courtesy of: https://wwfsassi.co.za/fish-detail/44/)

“Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Answered: (d) Determine the (i) critical points…

(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).

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 1EA: Suppose that a particular plot of land can sustain 500 deer and that the population of this...

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Question

Please help with D and E

(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?

Suppose that the differential equation
dy
dt
= y(40-y) - 300
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
Figure 1: The spotted grunter. (Image courtesy of: https://wwfsassi.co.za/fish-detail/44/)

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