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Population Growth Other Models Gompertz Example 1: Part 2
In this video I go over part 2 of the Example 1 on the Gompertz Function, which is the solution to the differential equation dP/dt = c*ln(K/P)*P, and is used to model population growth. In this part 2 video, I go over question d) of the example, which asks to show that the growth rate is fastest when the population is equal to K/e, compared with K/2 for the logistic model for population growth. In solving this, I use the first derivative test for local max and min but this time apply it for finding the maximum value of the derivative of population, which is the population growth rate.
Also in this video I go over a brief history on Benjamin Gompertz, the British Mathematician that published this population growth model, as well as some notable facts about his life and the use of the Gompertz Function. So make sure to watch this video!!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtlQMsoPCjT3Nd-5fg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/population-growth-other-models-gompertz-example-1-part-2
Related Videos:
Population Growth: Other Models: Example 3: Extinction: https://youtu.be/Pa6UTdh2r9M
Population Growth: Other Models: Harvesting: Example 2: https://youtu.be/jNAYTNhpZzk
Population Growth: Other Models: Harvesting: Example 1 Part 2: https://youtu.be/l1n6WUOxYCs
Population Growth: Other Models: Harvesting: Example 1 Part 1: https://youtu.be/ZLQEJwViIw0
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
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0
Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI
Differential Equations: Population Growth: Logistic Equation: Example 4: https://youtu.be/vS2qba4ucQY
Differential Equations: Population Growth: Logistic Equation: Example 2: https://youtu.be/vvL1STfPRkY
First Derivative Test: http://youtu.be/9W4ejz0EMtE .
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