 Exponential growth

A positive quantity undergoes exponential growth at constant rate $r>0$ when $y^{\prime }=ry$. For $y_0>0$, the solution of a differential equation is $y(t)=y_0{e}^{rt}$. Every interval of duration $\Delta t$ multiplies the value by the same factor $e^{r\Delta t}$, independently of its starting value.

Exponential growth refers to a process where the quantity increases at a rate proportional to its current value. This means that the larger the quantity becomes, the faster it grows.