$y$ is a function of $t$. Simple differential equations are written to make
$ \frac{dy}{dt} = ky(t) $
The function $y(t)$ that fits this is
$y(t) = y(0) e^{kt} $
Where $y(0)$ is some initial condition.
$ \frac{d}{dt} y(t) = k y(0) e^{kt} $
Achieving our constraint $ \frac{dy}{dt} = ky(t) $
This is all fine and dandy, but I'm wondering if anyone ever uses $2^{kt}, 3^{kt}$ or $n^{kt}$ in any problems. There is an accumulating $ln(2)$ factor on each derivative, but I'm wondering if that's ever useful.