\begin{frame} \frametitle{Exponential Population Growth} \begin{exampleblock}{} Let $y$ be the size of a population. \end{exampleblock} \pause\medskip Instead of saying `the growth rate is proportional to the size' \begin{talign} y' = ky \end{talign} \pause we can equivalently say that the \emph{relative growth rate} \begin{talign} \frac{y'}{y} = k &&\mpause[1]{\text{ or equivalently }}&&\mpause[1]{\frac{1}{y}\frac{dy}{dt} = k} \end{talign} is constant. \pause\pause\bigskip Then the solution is of the form \begin{talign} y = Ce^{kt} \end{talign} \end{frame}