Exponential Modelling

Exponential models usually take the form $A=A_0{e}^{kt}$. Here $A_0$ is the initial amount (at $t=0$), and $k$ controls the rate: positive $k$ is growth, negative $k$ is decay.

Substitute the given time $t$ to find the amount, or the initial value by setting $t=0$ (which makes $e^0=1$).

The constant in the front is the initial value; the sign of the exponent constant tells you growth vs decay; its size controls how fast. As $t\to \infty$, a decay model tends to $0$ while a growth model increases without bound.