Logistic Equation

[kaloryfer]

Why this equation does not fit the logistic model? Is it because the "t" should be a y?

 

[skeeter]

View attachment 23205
Why this equation does not fit the logistic model? Is it because the "t" should be a y?

yes, the solution is a cubic function

[MATH]\dfrac{dy}{dt} = \dfrac{t}{20}-\dfrac{t^2}{10^5}[/math]
[MATH]y= \dfrac{t^2}{40} - \dfrac{t^3}{3 \cdot 10^5} + C [/MATH]

 

[Steven G]

dy/dt means that what you are taking the derivative of should be in terms of t. Therefore the derivative of this function (dy/dt) should be in terms of t-not in terms of y.

 

[Deleted member 4993]

View attachment 23205
Why this equation does not fit the logistic model? Is it because the "t" should be a y?

What is the major characteristic of a logistic growth model?

at a certain point, growth steadily slows and the function approaches an upper bound, or limiting value.​

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The function has a horizontal asymptote. \(\displaystyle \lim_{t \to \infty}{\frac{dy}{dt}} \ = 0 \ \)​

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The general solution of a logistic model should be something like:

\(\displaystyle y \ = \ \dfrac{c}{1 \ + \ a *e^{-b * t}}\)

So the given DE does not fit logistic growth model because for the given DE \(\displaystyle \lim_{t \to \infty}{\frac{dy}{dt}} \ \ne 0 \ \)