Table 1.

Growth laws.

growth law	$\dot{x}=k{x}^p,p>0$
general solution	$x(t)=\{\begin{array}{c}{\left[x_0^{1-p}+(1-p)kt\right]}^{1/1-p}\text{for}p\ne 1\\ x(t)=x_0{\text{e}}^{kt}\text{for}p=1\end{array}$
particular cases	p=0: constant
	p=1/2: pure parabolic
	p=1: exponential
	p=2: pure hyperbolic