## Precalculus (6th Edition) Blitzer

The mathematical model for exponential growth or decay is given by $f(t)= A_{0}e^{kt}$ or $A= A_{0}e^{kt}$. If $k \gt 0$, the function models the amount of a growing entity. $A_{0}$ is the original amount, or size, of the growing entity at time t = 0, $A$ is the amount at time $t$, and $k$ is a constant representing the growth rate. If k $\lt$ 0, the function models the amount of a decaying entity ---- We see that countries with negative k are Japan and Russia.