Gompertz function

The Gompertz function is an asymmetrical saturation function. It is named after its discoverer, the British mathematician Benjamin Gompertz .

The function

The general formula of the Gompertz function is:

${\displaystyle y(t)=ae^{-be^{-ct}}}$

• ${\displaystyle a}$is the upper asymptote because of . ${\displaystyle \lim _{t\to \infty }ae^{-be^{-ct}}=ae^{0}=a}$ ${\displaystyle -c<0}$
• ${\displaystyle b,c}$ are positive numbers
• ${\displaystyle b}$is the shift ${\displaystyle t}$
• ${\displaystyle c}$ is the growth rate
• ${\displaystyle e}$is Euler's number ( ) ${\displaystyle e=2{,}71828\ldots }$

Variations of the variables

• 

  Variations of ${\displaystyle a}$

• 

  Variations of ${\displaystyle b}$

• 

  Variations of ${\displaystyle c}$

application

The Gompertz function is used in biology (e.g. to describe the growth of tumors) and in economics (e.g. in empirical trend research ).

See also

• Gompertz Makeham model

Individual evidence

1. ↑ Gompertz function in the function type library ( Memento from September 13, 2014 in the Internet Archive )