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A population of fish in a controlled pond is represented by a growth logistic model: Given the equation is: Pn+1 = 1.6P - 0.0003P,² where P, is the population at n-month. a) Find the value of rand M. Interpret your answers. (Hint: Hint: Pn+1 = P + rP (1-1 = P₁ + rP₂ ( 1 - where M is the carrying capacity) b) Given the initial fish population is 200. Find the population of the fish at P₁, P2, and P3. c) Sketch the solution of this model. What will happen to the population after a long time t. d) Find the equilibrium points of the given model and determine the solution's behaviour near the equilibrium points.

A population of fish in a controlled pond is represented by a growth logistic model: Given the equation is: Pn+1 = 1.6P - 0.0003P,² where P, is the population at n-month. a) Find the value of rand M. Interpret your answers. (Hint: Hint: Pn+1 = P + rP (1-1 = P₁ + rP₂ ( 1 - where M is the carrying capacity) b) Given the initial fish population is 200. Find the population of the fish at P₁, P2, and P3. c) Sketch the solution of this model. What will happen to the population after a long time t. d) Find the equilibrium points of the given model and determine the solution's behaviour near the equilibrium points.

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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A population of fish in a controlled pond is represented by a growth logistic model: Given the equation is: Pn+1 = 1.6P - 0.0003P, ² where P, is the population at n-month. a) Find the value of r and M. Interpret your answers. (Hint: Pn+1 = Pn + rPn (1- (1-2), where M is the carrying capacity) b) Given the initial fish population is 200. Find the population of the fish at P₁, P₂, and P3. c) Sketch the solution of this model. What will happen to the population after a long time t. d) Find the equilibrium points of the given model and determine the solution's behaviour near the equilibrium points.
Transcribed Image Text:A population of fish in a controlled pond is represented by a growth logistic model: Given the equation is: Pn+1 = 1.6P - 0.0003P, ² where P, is the population at n-month. a) Find the value of r and M. Interpret your answers. (Hint: Pn+1 = Pn + rPn (1- (1-2), where M is the carrying capacity) b) Given the initial fish population is 200. Find the population of the fish at P₁, P₂, and P3. c) Sketch the solution of this model. What will happen to the population after a long time t. d) Find the equilibrium points of the given model and determine the solution's behaviour near the equilibrium points.
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