Logistic Function
Logistic Function
\[y = \frac{L}{1+ae^{-kx}}\]
Variables
y = function value
L = maximum limit value
a = scaling constant
k = growth rate constant
x = independent variable
Description
What is this formula?
This formula models logistic growth, where growth starts exponentially and then slows as the function approaches a maximum limit.
When to use it
Use this formula for systems with limited growth capacity or saturation effects.
Example
For:
L=100
a=9
k=0.5
x=4
y=100/(1+(9*(℮^(-0.5*4))))
y≈45.09
Applications
Population dynamics
Biological growth
Machine learning
Epidemiology
Chemical reactions
Market adoption models
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