Exponential growth
= Exponential growth
{title2=$y(t)=y_0e^{rt},\quad r>0$}
{wiki}
A positive quantity undergoes <exponential growth> at constant rate $r>0$ when $y'=ry$. For $y_0>0$, the <solution of a differential equation> is $y(t)=y_0e^{rt}$. Every interval of duration $\Delta t$ multiplies the value by the same factor $e^{r\Delta t}$, independently of its starting value.