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Problem 17. Consider the logistic equation = 0.001P (200 – P) where t is measured in months. dt a. Without solving the equation, describe the behavior of the solution with an initial population of 50.

Problem 17. Consider the logistic equation = 0.001P (200 – P) where t is measured in months. dt a. Without solving the equation, describe the behavior of the solution with an initial population of 50.

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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dP Problem 17. Consider the logistic equation 0.001P (200 – P) where t is measured in months. dt a. Without solving the equation, describe the behavior of the solution with an initial population of 50.
Transcribed Image Text:dP Problem 17. Consider the logistic equation 0.001P (200 – P) where t is measured in months. dt a. Without solving the equation, describe the behavior of the solution with an initial population of 50.
Expert Solution
Step 1

The rate of change of population is 

-0.001p2+0.2p

Since the coefficient of p2 is negative so it will be a downward-facing parabola

So from starting First the population will rise till population becomes 100 but then after that, it will decrease continuously.

That means the population is going to wipe out after some year.

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