\begin{frame}
  \frametitle{Exponential Population Growth}

  \begin{exampleblock}{}
    The world population was
    \begin{itemize}
      \item 2560 million in 1950, and
      \item 3040 million in 1960.
    \end{itemize}
    Assume a constant growth rate. Find a formula $P(t)$ with
    \begin{itemize}
      \item $P(t)$ in millions of people and
      \item $t$ in years since 1950.
    \end{itemize}
    \pause
    We have
    \begin{talign}
      &P(t) = P(0) e^{kt} \\
      &\mpause[1]{P(0) = 2560}\\
      &\mpause[2]{P(10) = 2560 e^{10k} = 3040}\\
      &\mpause[3]{e^{10k} = \frac{3040}{2560}}
      \mpause[4]{\;\;\implies\;\; k = \frac{1}{10}\ln \frac{3040}{2560} \approx 0.017}
    \end{talign}
    \pause\pause\pause\pause\pause
    The world population growths with a rate of $1.7\%$ per year.
  \end{exampleblock}
\end{frame}