Exponential models

The idea

Growth and decay are modelled by $y = Ae^{kt}$: $A$ is the starting value and $k$ the rate ($k > 0$ grows, $k < 0$ decays). In $y = c + Ae^{-kt}$, the value levels off at $c$.

1. Put $t = 0$ to read the starting value.
2. Use a known pair of values and $\ln$ to find $k$.
3. Interpret: the long-run value, and whether the model stays sensible.

Watch out Check the model in context: no population grows for ever.