Process

Descriptive function

Comparative function

Decomposition, breakdown

$x=x_{\infty }{\text{e}}^{-ct}$

$\ln \frac{x_{\infty }}{x}$

Infinite proliferation

$x=x_{\infty }{\text{e}}^{ct}$

$-\ln \frac{x_{\infty }}{x}$

Logistic process by Fermi distribution

$x=1-\frac{x_{\infty }}{1+{\text{e}}^{-ct}}$

$\ln \frac{1-x}{x_{\infty }+x-1}$

Logistic process by Gompertz distribution

$x=x_{1\infty }{\text{e}}^{-x_{2\infty }{\text{e}}^{-ct}}$

$\ln \frac{x_{2\infty }}{\ln \frac{x_{1\infty }}{x}}$

Demographic explosion

$x=\frac{x_{\infty }}{\text{π}}\text{arccot}\left(ct\right)$

$\cot \frac{x}{x_{\infty }}\text{π}$