Population Growth: Other Models: Harvesting: Example 1 Part 1

Math Easy Solutions

First published at 17:02 UTC on April 16th, 2018.

In this video I look at the an example of a modification of the logistic equation by accounting adding a negative constant to the differential population growth formula. This negative constant can be used to model the harvesting of fish, which is simply a constant rate of fishing. Adding this to the logistic equation will result in a case where there are two none-zero equilibrium solutions. When the initial fish population is below the lowest equilibrium solution value, in this example it is a population of 250 fish, than the given constant fishing rate of 15 per week is in fact a case of overfishing, and thus the population goes to zero in time. This is the major difference that adding the harvesting constant adds to the logistic differential equation. I will solve this equation explicitly in the next video and compare the solution with that of the direction field graphed in this video, so stay tuned!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtVqJBMEixvPlKZi1g

Related Videos:

Population Growth: Introduction to Other Models: https://youtu.be/-l5Anv9VA3M
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Differential Equations: Logistic Equation: Analytic Solution: https://youtu.be/BlvLWTSYDDk
Differential Equations: Population Growth: Logistic Equation: https://youtu.be/yE8aoY8Bks4
Differential Equations: Population Growth: Proportionality Constant: https://youtu.be/y4cJX0rcXqw
Differential Equations: Exponential Growth and Decay: https://youtu.be/DZtDUIZuxcg
Differential Equations: Separable Equations: https://youtu.be/pBV-xT9ty94
Differential Equations: Euler's Method: https://youtu.be/VlwVl-3oPDM
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac .


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