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\begin{frame}

\begin{exampleblock}{}
Let $m(t)$ be the mass of a radioactive substance after time $t$.
\end{exampleblock}
\pause\medskip

Then the \emph{relative decay rate} rate
\begin{talign}
-\frac{m'}{m} = k &&\mpause[1]{\text{ or equivalently }}&&\mpause[1]{-\frac{1}{m}\frac{dm}{dt} = k}
\end{talign}
is constant.
\pause\pause\bigskip

Then the solution is of the form
\begin{talign}
m = Ce^{-kt}
\end{talign}
\pause\bigskip

Physicists typically express the decay in terms of half-life.
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\begin{block}{}
The \emph{half-life} is the time until only half of the quantity is left.
\end{block}
\end{frame}