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z0BY9clmOdW`ffSE2AxZ4a(+rGs8v*40&Mo>a#h@tJ!LI+kU_%b;miux2^Ghcxt>R~ z9SSQcTM!)8xOd4Eq1liAb-lln8rWrUOZn^x8`^Go8#72g|V*7Z~UyB8ZZBsLG=+2mTgtVC5c5P V6-B^sGzAWJ8F8tqy863u0RZm?es}-? literal 0 HcmV?d00001 diff --git a/PreStSauveur/Tsti2d/Suites/annales.tex b/PreStSauveur/Tsti2d/Suites/annales.tex new file mode 100644 index 0000000..1e462cd --- /dev/null +++ b/PreStSauveur/Tsti2d/Suites/annales.tex @@ -0,0 +1,53 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +\title{Annales} +\tribe{Terminale STI2D} +\date{Septembre 2018} + +\renewcommand{\arraystretch}{1} + +\begin{document} + +\begin{exercise}[subtitle={Population de renard (Polynésie 2017)}] +Dans un parc régional, on étudie une espèce de renards. Cette population était de 1240 renards à la fin de l’année 2016. + +On modélise par $u_n$le nombre de renards dans le parc régional à la fin de l'année 2016 + n. On a donc $u_0= 1240$. + +On estime à 15\% par an la baisse du nombre $u_n$. + +On suppose que cette évolution restera identique pour les années à venir. + +\begin{enumerate} + \item Montrer qu’à la fin de l’année 2017, la population de renards sera de 1054. + \item + \begin{enumerate} + \item Donner la valeur de $u_1$ puis calculer $u_2$. + \item Exprimer $u_{n+1}$ en fonction de $u_n$. + \item En déduire la nature de la suite $(u_n)$ et préciser ses éléments caractéristiques. + \end{enumerate} + \item Déterminer une estimation du nombre de renards présents dans le parc régional à la fin de l’année 2020. + \item Des scientifiques considèrent que l’espèce des renards présents dans le parc sera en situation d’extinction à partir du moment où le nombre de renards deviendra strictement inférieur à 100. + À partir de quelle année l'espèce de renards présents dans le parc sera-t-elle en situation d'extinction? +\end{enumerate} + + +\end{exercise} + +\begin{exercise}[subtitle={Aquarium (Métropole 2018)}] + Après son installation, un lundi matin, un aquarium contient 280 litres d’eau et des poissons. Par évaporation, le volume d’eau dans l’aquarium diminue de 2\% par semaine. Compte tenu du nombre de poissons, cet aquarium doit contenir en permanence au minimum 240 litres d’eau. + + \begin{enumerate} + \item Quel volume d’eau restera-t-il dans l’aquarium au bout d’une semaine ? + \item Est-il vrai qu’au bout de deux semaines, exactement 4\% du volume d’eau initial se seront évaporés ? Justifier. + \item Déterminer au bout de combien de semaines le volume d’eau dans l’aquarium deviendra insuffisant. + \end{enumerate} +\end{exercise} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: +