13/99
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\frametitle{Exponential Growth and Decay}

Often quantities grow or decay proportional to their size:
\begin{itemize}
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\item growth of a population (animals, bacteria,\ldots)
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\item growth of savings on your bank account (interest rates)
\end{itemize}
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Assume that
\begin{itemize}
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\item $y(t)$ be a quantity depending on time $t$
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\item rate of change of $y(t)$ is proportional to $y(t)$
\end{itemize}
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Then
\begin{talign}
y' = ky &&\mpause[1]{\text{or equivalently}} && \mpause[1]{\frac{d}{dt}y = ky}
\end{talign}
where $k$ is a constant. \pause\pause This equation is called:
\begin{itemize}
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\item \emph{law of natural growth} if $k > 0$
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\item \emph{law of natural decay} if $k < 0$
\end{itemize}
\end{frame}