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\begin{frame}
\frametitle{Newtons Law of Cooling/Warming}

\begin{block}{Newtons Law of Cooling}
The rate of cooling of an object is proportional to the
temperature difference of the object and surrounding temperature.
\end{block}
\pause\medskip

Let
\begin{itemize}
\pause
\item $T(t)$ be the temperature after time $t$, and
\pause
\item $T_s$ the temperature of the surroundings.
\end{itemize}
\pause\medskip

Then the law can be written as differential equation:
\begin{talign}
T'(t) = k(T(t) - T_s)
\end{talign}
where $k$ is constant.
\pause\medskip

This is not yet the form that we need. Let
\begin{talign}
y(t) = T(t) - T_s &&\mpause[1]{then} &&\mpause[1]{y'(t) = T'(t)}
&&\mpause[2]{thus} &&\mpause[2]{y'(t) = ky(t)}
\end{talign}
\pause\pause\pause
Thus the solution for $y$ is an exponential function $Ce^{kt}$.
\end{frame}