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\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}
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