\begin{frame}
  \frametitle{Exponential Functions: Applications}
  
  \begin{exampleblock}{}
    We consider a population of bacteria:
    \begin{itemize}
      \item suppose the population doubles every hour
      \item we write $p(t)$ for the population after $t$ hours
      \item initial population is $p(0) = 1000$
    \end{itemize}
  \end{exampleblock}
  \pause
  
  We have:
  \begin{talign}
    &\mpause[1]{p(1) = 2\cdot p(0) = 2\cdot 1000}\\
    &\mpause[2]{p(2) = 2\cdot p(1) = 2^2\cdot 1000}\\
    &\mpause[3]{p(3) = 2\cdot p(2) = 2^3\cdot 1000}\\[-1ex]
    &\mpause[4]{\hspace{2cm}\vdots}
  \end{talign}
  \pause[6]
  Thus in general
  \begin{talign}
    p(t) = 1000\cdot 2^t
  \end{talign}
  \vspace{-2ex}\pause
  \begin{exampleblock}{}
    Under ideal conditions such rapid growth occurs in nature.
  \end{exampleblock}
\end{frame}