## College Algebra (6th Edition)

Logistic growth: growth is limited. Exponential growth$:$ growth is not limited.
Exponential growth model: $A=A_{0}e^{kt} \quad (k>0)$ (where $A_{0}$ is the initial quantity, and $A$ is the quantity after time t) The growth is unlimited, A can become arbitrarily large. ----------- The logistic growth model, given by $A=\displaystyle \frac{c}{1+ae^{-bt}}$, (a,b,c are constants and $c>0, b>0$) describes situations in which growth is limited. $y=c$ is a horizontal asymptote for the graph, and growth, $A$, can never exceed $c$.