2022-2023/2nd/14_Information_Chiffree_2/2B_coef_mult.tex

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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\author{Benjamin Bertrand}
\title{Information chiffrée 2 - Cours}
\date{Mars 2023}
\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}