Extended Answer Question 3Consider a population of marine fish in a reef with and intrinsic growth rate of 0.5 per year and acarrying capacity of 100 thousands. Let p(t) be the population of fish (in thousands) at time I (inyears). Assume that it can be modelled using the logistic model. Furthermore, assume that fishing isallowed at a constant rate of 8000 per year.a) Write down the appropriately modified logistic model differential equation for p(I).b) Without solving the differential equation, sketch the graph of the particular solution of thedifferential equation in a), satisfying p(0) = 40. Indicate inflection points if there are any.%3Dc) Find the explicit particular solution satisfying p(0) = 40. What is its limit as t 0o?d) Find all values of a for which the equality p(0) = a implies extinction for the marine fish.

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Answered: Consider a population of marine fish in…

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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