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A fish farm stocks its lake with 350 fish prior to commencing operations. The farm management company observes that the number of fish p at any time t days after commencement of operations satisfies the differential equation dp dt p(600 — р) — 5000 (p20). (a) Determine the equilibrium solution(s) for the population model. (b) Draw a phase plot, dp versus p. Label any intercept with the p-axis. dt (c) Sketch p versus t for the given initial condition. Label any intercept with the p-axis, any asymptote, and the population at any inflection point.

A fish farm stocks its lake with 350 fish prior to commencing operations. The farm management company observes that the number of fish p at any time t days after commencement of operations satisfies the differential equation dp dt p(600 — р) — 5000 (p20). (a) Determine the equilibrium solution(s) for the population model. (b) Draw a phase plot, dp versus p. Label any intercept with the p-axis. dt (c) Sketch p versus t for the given initial condition. Label any intercept with the p-axis, any asymptote, and the population at any inflection point.

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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Question 7 A fish farm stocks its lake with 350 fish prior to commencing operations. The farm management company observes that the number of fish p at any timet days after commencement of operations satisfies the differential equation dp dt = p(600 – p) – 50000 (p20). (a) Determine the equilibrium solution(s) for the population model. dp versus p. Label any intercept with the p-axis. dt (b) Draw a phase plot, (c) Sketch p versus t for the given initial condition. Label any intercept with the p-axis, any asymptote, and the population at any inflection point.
Transcribed Image Text:Question 7 A fish farm stocks its lake with 350 fish prior to commencing operations. The farm management company observes that the number of fish p at any timet days after commencement of operations satisfies the differential equation dp dt = p(600 – p) – 50000 (p20). (a) Determine the equilibrium solution(s) for the population model. dp versus p. Label any intercept with the p-axis. dt (b) Draw a phase plot, (c) Sketch p versus t for the given initial condition. Label any intercept with the p-axis, any asymptote, and the population at any inflection point.
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