The Gompertz Sigmoid Function and Its Derivative
The Gompertz Sigmoid Function and Its Derivative
This Gompertz function is defined by or , where is the upper asymptote and and are the negative growth rates. The Gompertz function is a sigmoid function. It is a type of mathematical model for a time series, where growth is slowest at the start and end of a time period. This Demonstration plots the Gompertz function , its derivative, , and the ratio ln(f(t))= .
f(t)=a
b
ct
e
e
f(t)=aexp(bexp(ct))
a
b
c
f(t)
f'(t)=abc
b
ct
e
e
ct
e
d
dt
f'(t)/f(t)