Growth model

Differential equation

Integrated equation

Gompertz

$G=-a\ln \left(S\right)+b$

$S=S_{\infty }\exp \left[-\exp -a\left(t+t_0\right)\right]$

or $S=S_{\infty }\exp \left[-b\exp \left(-at\right)\right]$

Logistique

$G=-aS+b$

$S=S_{\infty }{\left[1+\exp -b\left(t+t_0\right)\right]}^{-1}$

Von Bertalanffy

$G=a\frac{1}{S}-b$

$S=S_{\infty }\left[1-\exp -b\left(t+t_0\right)\right]$