DSED Support Question 4 Suppose that the differential equation dy dE = y(40-y) - 300 models a logistic equation with harvesting, where you) represents a spotted grunter population in the Knysna Lagoon at time t, measured in years. Write down the (a) per capita growth rate of the spotted grunter population (b) carrying capacity of the Lagoon. (a rate at which the spotted Lagan grunter are harvested from the Lagoon d) Determine the i criticell 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) & Taking y(0) = 11 and a step size b of h=1/12 apply Four iterations of the forward Euler Formula to approximate the solution of Eq. (3). Apply two decinal place rounding where applicable
DSED Support Question 4 Suppose that the differential equation dy dE = y(40-y) - 300 models a logistic equation with harvesting, where you) represents a spotted grunter population in the Knysna Lagoon at time t, measured in years. Write down the (a) per capita growth rate of the spotted grunter population (b) carrying capacity of the Lagoon. (a rate at which the spotted Lagan grunter are harvested from the Lagoon d) Determine the i criticell 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) & Taking y(0) = 11 and a step size b of h=1/12 apply Four iterations of the forward Euler Formula to approximate the solution of Eq. (3). Apply two decinal place rounding where applicable
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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Question 4
Suppose that the differential equation
dy
dt = y(40-y) - 300
models a logistic equation with harvesting, where y(t)
represents a spotted grunter population in the Knysna
Lagoon at time t, measured in years.
Write down the
(a) per capita growth rate of the spotted grunter
population
(b) carrying capacity of the Lagoon.
(e rate at which the spotted Lagoon grunter are
harvested from the Laigeon
el Determine the
Ii criticell points of Eq. (3)
(ii) limiting and threshole solutions from Eq. (3)
(iii) stability of the critical points by drawing a phase
diagram For Eq= (3)
e) & Taking y(a) = 11 and a step size b of h=1/12
apply four iterations of the forward Euler formulet
to approximate the solution of Eq. (3). Apply two
decinal place rounding where applicable
(i) How do your results from (e) i) compare with what
the phase clíagram for Eq. (3) reveals?
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