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\begin{frame}
  \frametitle{Exponential Functions vs. Power Functions}

  \begin{exampleblock}{}
    Which functions grows quicker when $x$ is large:
    \begin{talign}
      f(x) &= 10\cdot x^5 & g(x) = 1.1^x
    \end{talign}
  \end{exampleblock}
  \bigskip\pause
  
  \begin{center}
  \only<-3>{
  \begin{minipage}{.59\textwidth}
  \scalebox{.7}{
  \begin{tikzpicture}[default,baseline=0cm,xscale=1,yscale=.1,nodes={scale=.9}]
    {\def\diaborderx{1cm}
     \def\diabordery{5cm}
     \diagram[5]{-0.5}{6}{-.5}{40}{1}
    }
    \diagramannotatez
    \diagramannotatex{5}
    \diagramannotatey{10,20,30}
    \begin{scope}[ultra thick]
    \draw[cblue] plot[smooth,domain=-0:5.31,samples=100] (\x,{1.1^\x}) node[above] {$1.1^x$};
    \draw[cgreen] plot[smooth,domain=-0:1.32,samples=100] (\x,{10*\x^5}) node[above] {$10*x^5$};
    \end{scope}
  \end{tikzpicture}
  }
  \end{minipage}\pause
  \begin{minipage}{.4\textwidth}
  \scalebox{.7}{
  \begin{tikzpicture}[default,baseline=0cm,xscale=.05,yscale=.01,nodes={scale=.9}]
    {\def\diaborderx{15cm}
     \def\diabordery{50cm}
     \diagram[50]{-0.5}{65}{-.5}{400}{1}
    }
    \diagramannotatez
    \diagramannotatex{50}
    \diagramannotatey{100,200,300}
    \begin{scope}[ultra thick]
    \draw[cblue] plot[id=onedotone,smooth,domain=-0:63,samples=100] function{1.1**x} node[above] {$1.1^x$};
    \draw[cgreen] plot[id=xfive,smooth,domain=-0:2.1,samples=100] function{10*x**5} node[above] {$10*x^5$};
    \end{scope}
  \end{tikzpicture}
  }
  \end{minipage}
  }
  \pause
  \begin{minipage}{.6\textwidth}
  \scalebox{.8}{
  \begin{tikzpicture}[default,baseline=0cm,xscale=.1,yscale=.01,nodes={scale=.9}]
    {\def\diaborderx{12cm}
     \def\diabordery{50cm}
     \diagram[50]{-0.5}{50}{-.5}{400}{1}
    }
    \diagramannotatez
    \diagramannotatexx{10/$100$,20/$200$,30/$300$,40/$400$}
    \diagramannotateyy{100/$1\cdot 10^{15}$,200/$2\cdot 10^{15}$,300/$3\cdot 10^{15}$}
    \begin{scope}[ultra thick]
    \draw[cblue] plot[id=onedotone,smooth,domain=-0:37.7,samples=100] function{1.1**(10*x)/10000000000000} node[above] {$1.1^x$};
    \draw[cgreen] plot[id=xfive,smooth,domain=-0:50,samples=100] function{10*(10*x)**5/10000000000000} node[above,xshift=5mm] {$10*x^5$};
    \end{scope}
  \end{tikzpicture}
  }
  \end{minipage}
  \end{center}
  \pause\pause\bigskip
  
  \begin{block}{}
    For any $1 < a$, the \emph{exponential function} $f(x) = a^x$
    grows for large $x$ much \emph{faster than any polynomial}.
  \end{block}
  
  \vspace{10cm}
\end{frame}