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

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

\pagestyle{empty}

\begin{document}

\maketitle


\section*{Lien entre taux d'évolution et coefficient multiplicateur}

\begin{propriete}
    Soit $t$ le taux d'évolution qui fait évolution $v_i$ vers $v_f$ alors
    \[
        v_f = (1+t)v_i
    \]
\end{propriete}
\begin{definition}
    $1+t$ est appelé \textbf{coefficient multiplicateur}, noté $CM$, associé au taux d'évolution $t$.

    \noindent
    On a ainsi
    \[
        CM = 1+t \qquad \mbox{ou encore} \qquad t = CM - 1
    \]
    et
    \[
        v_f = CM \times v_i \qquad \mbox{ ou encore } \qquad CM = \frac{v_f}{v_i}
    \]
\end{definition}
\paragraph{Exemples}
\begin{itemize}
    \item 
        \begin{tikzpicture}[
            baseline,
            roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
            arrow/.style={->, shorten >=5pt, shorten <=5pt}
            ]
            %Nodes
            \node[roundnode]        (leftterme)       {\makebox[0.5cm]{120}};
            \node[roundnode]        (centerterm)      [right=2cm of leftterme] {\makebox[0.5cm]{...}};

            %Lines
            \path[arrow] (leftterme.north) edge [bend left]
                node [pos=0.5, above] {+25\%}
                node [pos=0.5, below] {\times CM = ...}
                (centerterm.north)
                ;
        \end{tikzpicture}
        Coefficient multiplicateur: \hfill Valeur finale: \hfill.
    \item 
        \begin{tikzpicture}[
            baseline,
            roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
            arrow/.style={->, shorten >=5pt, shorten <=5pt}
            ]
            %Nodes
            \node[roundnode]        (leftterme)       {\makebox[0.5cm]{55}};
            \node[roundnode]        (centerterm)      [right=2cm of leftterme] {\makebox[0.5cm]{...}};

            %Lines
            \path[arrow] (leftterme.north) edge [bend left]
                node [pos=0.5, above] {+...}
                node [pos=0.5, below] {\times 0.12}
                (centerterm.north)
                ;
        \end{tikzpicture}
        Taux d'évolution: \hfill Valeur finale: \hfill.
    \item 
        \begin{tikzpicture}[
            baseline,
            roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
            arrow/.style={->, shorten >=5pt, shorten <=5pt}
            ]
            %Nodes
            \node[roundnode]        (leftterme)       {\makebox[0.5cm]{34}};
            \node[roundnode]        (centerterm)      [right=2cm of leftterme] {\makebox[0.5cm]{123}};

            %Lines
            \path[arrow] (leftterme.north) edge [bend left]
                node [pos=0.5, above] {+...\%}
                node [pos=0.5, below] {\times ...}
                (centerterm.north)
                ;
        \end{tikzpicture}
        Taux d'évolution: \hfill Valeur finale: \hfill.
\end{itemize}

\afaire{Compléter les calculs}
\end{document}