In this video I go over the logistic differential equation, which is a more advanced version of the simple population growth exponential model that I went over in my earlier videos. The basic model involved the assumption that the growth rate is proportional to the population size but this is only true if the population size is small. As the population size gets larger, a relative growth rate decreases as it approaches the carrying capacity, which is the largest population size that can be maintained in the long run. If the population size ever gets larger than the carrying capacity, then the growth rate becomes negative since the environment won't have enough resources to maintain too large a population. The logistic equation takes all of these factors into consideration and it is written in terms of the differential equation:
dP/dt = kP(1 - P/K)
Where P is the population size, k is the proportionality constant, and K is the carrying capacity.
In my later videos I will build upon this logistic equation as well find solutions for such equations, so stay tuned for those!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtQWBtWhfGWVHv4AWg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-population-growth-logistic-equation
Related Videos:
Differential Equations: Population Growth: Proportionality Constant:
Differential Equations: Exponential Growth and Decay:
Differential Equations: Separable Equations:
Differential Equations: Euler's Method:
Differential Equations: Direction Fields:
Differential Equations: Population Growth: .
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I don't always model population growth but when I do I usually use the logistic differential equation to do so ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-population-growth-logistic-equation
Wuao these equations are not easy for me, but I like the videos I try to understand a bit
I congratulate you @mes that well prepared these with the mathematics not everyone has that knowledge