1. A fish hatchery employed a mathematician to design a model to predict the population size of fish that the hatchery can expect to find in their pond at any given time. The mathematical model that the mathematician created is: dP/dt = 2P(1-(P/25))

1. A fish hatchery employed a mathematician to design a model to predict the population size of fish that the hatchery can expect to find in their pond at any given time. The mathematical model that the mathematician created is: dP/dt = 2P(1-(P/25))

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

dP/dt = 2P(1-(P/25))

(a) Draw a one dimensional phase portrait of the autonomous differential equation. What does this differential equation predict for future fish populations for various initial conditions? Describe the various cases in a few sentences interpreting your one-dimensional phase diagram.

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