\frametitle{Exponential Radioactive Decay}
    Let $m(t)$ be the mass of a radioactive substance after time $t$.
  Then the \emph{relative decay rate} rate 
    -\frac{m'}{m} = k &&\mpause[1]{\text{ or equivalently }}&&\mpause[1]{-\frac{1}{m}\frac{dm}{dt} = k}
  is constant.

  Then the solution is of the form
    m = Ce^{-kt}

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