\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}

\author{Benjamin Bertrand}
\title{Information chiffrée 2- Cours}
\date{2022-01-13}

\pagestyle{empty}

\begin{document}

\maketitle

\section*{Taux d'évolution successifs}

\begin{propriete}
    Quand une quantité subit des \textbf{évolution successives} $t_1, t_2, ...$, elle subit alors une \textbf{évolution globale}.

    Les taux d'évolution \textbf{ne peuvent pas} s'ajouter.

    \bigskip

    Il faut multiplier les \textbf{coefficient multiplicateur} entre eux.

    \begin{center}
        \begin{tikzpicture}[
            roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
            node distance=2cm and 2cm,
            arrow/.style={->, shorten >=5pt, shorten <=5pt}
            ]
            %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]{}};
            \node                   (termE)      [right=1cm of termD] {\makebox[0.5cm]{...}};
            \node[roundnode]        (termF)      [right=1cm of termE] {\makebox[0.5cm]{}};

            %Lines
            \path[arrow] (termA.north) edge [bend left=50] node [above]  {$+t_1$} node [below] {$\times CM_1$} (termB.north) ;
            \path[arrow] (termB.north) edge [bend left=50] node [above]  {$+t_2$} node [below] {$\times CM_2$} (termC.north) ;
            \path[arrow] (termC.north) edge [bend left=50] node [above]  {$+t_3$} node [below] {$\times CM_3$} (termD.north) ;

            \path[arrow] (termA.south) edge [bend right=10] node [above]  {Taux d'évolution global} node [below] {$\times CM_1 \times CM_2 \times CM_3 \times ...$} (termF.south);
        \end{tikzpicture}    
    \end{center}
\end{propriete}

\paragraph{Exemples:}
\begin{itemize}
    \item Une quantité a subit 5 augmentations de 10\%.
        \begin{center}
            \begin{tikzpicture}[
                roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
                arrow/.style={->, shorten >=5pt, shorten <=5pt}
                ]
                %Nodes
                \node[roundnode]        (termA)        {\makebox[0.5cm]{}};
                \node[roundnode]        (termB)      [right=2cm of termA] {\makebox[0.5cm]{}};
                \node[roundnode]        (termC)      [right=2cm of termB] {\makebox[0.5cm]{}};
                \node[roundnode]        (termD)      [right=2cm of termC] {\makebox[0.5cm]{}};
                \node[roundnode]        (termE)      [right=2cm of termD] {\makebox[0.5cm]{}};
                \node[roundnode]        (termF)      [right=2cm of termE] {\makebox[0.5cm]{}};

                %Lines
                \path[arrow] (termA.north) edge [bend left=50] node [above]  {$+10\%$} node [below] {$\times ...$} (termB.north) ;
                \path[arrow] (termB.north) edge [bend left=50] node [above]  {$+10\%$} node [below] {$\times ...$} (termC.north) ;
                \path[arrow] (termC.north) edge [bend left=50] node [above]  {$+10\%$} node [below] {$\times ...$} (termD.north) ;
                \path[arrow] (termD.north) edge [bend left=50] node [above]  {$+10\%$} node [below] {$\times ...$} (termE.north) ;
                \path[arrow] (termE.north) edge [bend left=50] node [above]  {$+10\%$} node [below] {$\times ...$} (termF.north) ;

                \path[arrow] (termA.south) edge [bend right=10] node [above]  {Taux d'évolution global} node [below] {$\times ... \times ... \times ... \times ... \times ... = \times ...$} (termF.south);
            \end{tikzpicture} 
        \end{center}
        Le coefficient global est donc de $CM = ...$

        On en déduit le \textbf{taux d'évolution global} $t = ...$
    \item Une quantité a subit une augmentation de 5\% puis un diminution de 10\% et enfin une autre augmentation de 5\%. Calculons le taux d'évolution global.
\end{itemize}
\afaire{Compléter les exemples}

\end{document}
