\begin{frame}
  \frametitle{Exponential Growth and Decay}

  \begin{exampleblock}{}
  Assume that $y(t)$ be a function, and $k$ a constant such that
  \begin{talign}
    y' = ky
  \end{talign}
  \end{exampleblock}
  \pause\medskip

  We have seen functions with this behavior:
  \pause
  \begin{talign}
    y(t) = Ce^{kt} &&\mpause[1]{y'(t) = k(Ce^{kt})} \mpause[2]{= ky(t)}
  \end{talign}
  \pause\pause\pause
  Note that 
  \begin{talign}
    y(0) = Ce^0 = C
  \end{talign}
  \pause\vspace{-1ex}

  \begin{block}{}
    The only solutions of the differential equation
    \begin{talign}
      y' = ky
    \end{talign}
    are the exponential functions
    \begin{talign}
      y(t) = Ce^{kt}
    \end{talign}
    where $C$ is any real number.
  \end{block}
\end{frame}