<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,10pt]{article}
\usepackage{myXsim}
\usetikzlibrary{positioning}

\author{Benjamin Bertrand}
\title{Prolongement géométrique vers exponentiel - Exercices}
\date{Décembre 2020}

\DeclareExerciseCollection{banque}
\xsimsetup{
    step=4,
}

\begin{document}

\setcounter{section}{2}
\section{Taux d'évolution moyen}

\begin{definition}[Taux d'évolution moyen]
    \begin{minipage}{0.45\linewidth}
    On note $t_m$ le taux d'évolution et $T$ le taux d'évolution global et $n$ le nombre de 'sous-évolutions'. Alors
    \[
        1 + T = (1 + t_m)^n \qquad \qquad 1 + t_m = (1 + T)^{\frac{1}{n}}
    \]
        
    \end{minipage}
    \hfill
    \begin{minipage}{0.5\linewidth}
    \begin{tikzpicture}[
        roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
        node distance=2cm and 2cm
        ]
        %Nodes
        \node[roundnode]        (termA)        {\makebox[0.5cm]{}};
        \node[roundnode]        (termB)      [right=of termA] {\makebox[0.5cm]{}};
        \node[roundnode]        (termC)      [right=of termB] {\makebox[0.5cm]{}};
        \node[roundnode]        (termD)      [right=of termC] {\makebox[0.5cm]{}};

        %Lines
        \path[-&gt;] (termA.north) edge [bend left] node [above]  {$+t_m$} node [below] {$\times (1+t_m)$} (termB.north) ;
        \path[-&gt;] (termB.north) edge [bend left] node [above]  {$+t_m$} node [below] {$\times (1+t_m)$} (termC.north) ;
        \path[-&gt;] (termC.north) edge [bend left] node [above]  {$+t_m$} node [below] {$\times (1+t_m)$} (termD.north) ;
                                                                                                                     
        \path[-&gt;] (termA.south) edge [bend right] node [above]  {$+t_m$} node [below] {$\times (1+T)$} (termD.south);
    \end{tikzpicture}
    \end{minipage}
\end{definition}

\medskip
\hline

\input{exercises.tex}
\printcollection{banque}

\vfill

\setcounter{section}{2}
\section{Taux d'évolution moyen}

\begin{definition}[Taux d'évolution moyen]
    \begin{minipage}{0.45\linewidth}
    On note $t_m$ le taux d'évolution et $T$ le taux d'évolution global et $n$ le nombre de 'sous-évolutions'. Alors
    \[
        1 + T = (1 + t_m)^n \qquad \qquad 1 + t_m = (1 + T)^{\frac{1}{n}}
    \]
        
    \end{minipage}
    \hfill
    \begin{minipage}{0.5\linewidth}
    \begin{tikzpicture}[
        roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
        node distance=2cm and 2cm
        ]
        %Nodes
        \node[roundnode]        (termA)        {\makebox[0.5cm]{}};
        \node[roundnode]        (termB)      [right=of termA] {\makebox[0.5cm]{}};
        \node[roundnode]        (termC)      [right=of termB] {\makebox[0.5cm]{}};
        \node[roundnode]        (termD)      [right=of termC] {\makebox[0.5cm]{}};

        %Lines
        \path[-&gt;] (termA.north) edge [bend left] node [above]  {$+t_m$} node [below] {$\times (1+t_m)$} (termB.north) ;
        \path[-&gt;] (termB.north) edge [bend left] node [above]  {$+t_m$} node [below] {$\times (1+t_m)$} (termC.north) ;
        \path[-&gt;] (termC.north) edge [bend left] node [above]  {$+t_m$} node [below] {$\times (1+t_m)$} (termD.north) ;
                                                                                                                     
        \path[-&gt;] (termA.south) edge [bend right] node [above]  {$+t_m$} node [below] {$\times (1+T)$} (termD.south);
    \end{tikzpicture}
    \end{minipage}
\end{definition}

\medskip
\hline

\printcollection{banque}

\end{document}
</pre></body></html>