\begin{frame} \frametitle{Exponential Radioactive Decay} \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. \pause \begin{block}{} The \emph{half-life} is the time until only half of the quantity is left. \end{block} \end{frame}