\[y = ae^{-be^{-cx}}\]
Variables
yfunction value
aupper asymptote
bhorizontal displacement constant
cgrowth rate constant
xindependent variable
Description
What is this formula?
This formula represents the Gompertz growth model, a sigmoid-type function commonly used for asymmetric biological and statistical growth processes.
When to use it
Use this formula when modeling growth that starts slowly, accelerates and then gradually saturates asymmetrically.
Example
For:
a=100
b=5
c=0.4
x=6
y=100*(℮^(-5*(℮^(-0.4*6))))
y≈63.54
Applications
Tumor growth modeling
Population dynamics
Actuarial science
Biological growth
Epidemiology
Reliability analysis