\begin{frame}
  \frametitle{Exponential Functions: The Number $e$}

  \begin{block}{}
    The number 
    \begin{talign}
      e \approx 2.71828\ldots
    \end{talign}
    is a very special base for exponential functions.
  \end{block}
  \pause\bigskip
  
  \begin{minipage}{.49\textwidth}
  \begin{center}
  \scalebox{.8}{
  \begin{tikzpicture}[default,baseline=0cm]
    \diagram{-2.5}{1.5}{-.5}{4}{1}
    \diagramannotatez
    \diagramannotatexx{-1,1}
    \diagramannotatey{1}
    \begin{scope}[ultra thick]
    \draw[cgreen] plot[smooth,domain=-2.5:1.4,samples=300] (\x,{e^\x});
    \end{scope}
    \begin{scope}[dashed,thick]
    \tangent{2.5cm}{2.5cm}{e^\x}{0}
    \node[include=cred] at (0,1) {};
    \end{scope}
  \end{tikzpicture}
  }\\[.5ex]
  tangent has slope $1 = e^0$
  \end{center}
  \end{minipage}
  \begin{minipage}{.49\textwidth}
  \begin{center}
  \scalebox{.8}{
  \begin{tikzpicture}[default,baseline=0cm]
    \diagram{-2.5}{1.5}{-.5}{4}{1}
    \diagramannotatez
    \diagramannotatexx{-1,1}
    \diagramannotatey{1}
    \begin{scope}[ultra thick]
    \draw[cgreen] plot[smooth,domain=-2.5:1.4,samples=300] (\x,{e^\x});
    \end{scope}
    \begin{scope}[dashed,ultra thick]
    \tangent{3.5cm}{1.5cm}{e^\x}{1}
    \node[include=cred] at (1,{e}) {};
    \end{scope}
  \end{tikzpicture}
  }\\[.5ex]
  tangent has slope $e = e^1$
  \end{center}
  \end{minipage}
  \pause
  
  \begin{block}{}
    The slope of the function $e^x$ at point $(x,e^x)$ is $e^x$. 
  \end{block}
\end{frame}