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b/2nd/02_Information_chiffree_1/3B_evolution.tex new file mode 100644 index 0000000..ed88ef0 --- /dev/null +++ b/2nd/02_Information_chiffree_1/3B_evolution.tex @@ -0,0 +1,89 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Information chiffrée 1 - Cours} +\date{Septembre 2021} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\setcounter\section{1} +\section{Evolutions} + +Quand une quantité change, on peut décrire son évolution de deux manières + +\begin{definition}[Evolutions] + ~\\ + Soient une grandeur qui passe de $v_d$ à $v_a$. + \hfill + \begin{minipage}{0.5\linewidth} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) {\makebox[0.5cm]{$v_d$}}; + \node[roundnode] (centerterm) [right=of leftterme] {\makebox[0.5cm]{$v_a$}}; + + %Lines + \path[->] (leftterme) edge [bend left] (centerterm); + \end{tikzpicture} + \end{minipage} + \hfill + + + \begin{itemize} + \item On peut calculer la différence absolue: \[v_a - v_b\] + + La différence absolue est exprimée dans l'unité de la grandeur. + \item On peut calculer la différence relative ou encore \textbf{taux d'évolution} + \[ + t = \frac{v_a - v_d}{v_d} + \] + Le taux d'évolution est un nombre quelconque qui mis sous forme d'un pourcentage. + \end{itemize} +\end{definition} + +\paragraph{Exemple:} ~ +Le prix d'une robe est passé de 80\euro à 70\euro. +\begin{itemize} + \item Variation absolue: + \item Taux d'évolution: +\end{itemize} +\afaire{} + + +\begin{definition}[Coéfficient multiplicateur] + Une quantité vaut initialement $v$ et est transformée avec un taux d'évolution $t$. + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (leftterme) at (0, 0) {\makebox[0.5cm]{$v_d$}}; + \node[roundnode] (rightterm) at (4, 0) {\makebox[0.5cm]{$v_a$}}; + + %Lines + \path[->] (leftterme) edge [bend left] node [above] {+t} node [below] {$\times (1 + t)$} (rightterm); + \end{tikzpicture} + \end{center} + + Alors cette quantité est multipliée par + \[ + CM = (1 + t) + \] + On appelle la quantité $CM$ le coefficient multiplicateur. +\end{definition} + +\paragraph{Exemples:}~ +\begin{itemize} + \item Une usine produit 3millions de tonne de produit par an en 2020. En 2021, cette quantité a augmenté de 5\%. Elle est donc de + \afaire{} + \item Un vélo coûte 250\euro. Des soldes font baisser son prix de 20\%. On peut donc l'acheter + \afaire{} +\end{itemize} + +\end{document} diff --git a/2nd/02_Information_chiffree_1/index.rst b/2nd/02_Information_chiffree_1/index.rst index 724482b..c91f2e3 100644 --- a/2nd/02_Information_chiffree_1/index.rst +++ b/2nd/02_Information_chiffree_1/index.rst @@ -67,6 +67,11 @@ Ensuite on donne une série d'objet, seul puis en groupe, ils devront pour chaqu *Bilan*: Nécessité d'avoir une référence quand on parle de pourcentage, différentes façon de calculer les évolutions en pourcentages (avec le dessin) +.. image:: ./3B_evolution.pdf + :height: 200px + :alt: Bilan sur les taux d'évolutions + + Ils appliqueront ces méthodes en initiation à la programmation. - `TP version html <./3_initiation_programmation.html>`_