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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

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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(intel) inside Dolby Audio eSupport 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?
Transcribed Image Text:(intel) inside Dolby Audio eSupport 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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