Feat: reprise des docs d'ensSci (pas convaincu des changements)
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\author{Benjamin Bertrand}
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\title{Dérivation - exercices}
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\date{septembre 2020}
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\date{septembre 2021}
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\pagestyle{empty}
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\DeclareExerciseCollection{banque}
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\DeclareExerciseCollection[step=3]{banque}
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\xsimsetup{
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step=3,
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exercise/the-counter=2
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collect,
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exercise/the-counter=3
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}
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\begin{document}
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\author{Benjamin Bertrand}
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\title{Dérivation - exercices}
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\date{septembre 2020}
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\date{septembre 2021}
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\thispagestyle{empty}
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\DeclareExerciseCollection{banque}
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\DeclareExerciseCollection[step=4]{banque}
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\xsimsetup{
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step=4,
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exercise/the-counter=3
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collect,
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exercise/the-counter=4
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}
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\begin{document}
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\renewcommand{\arraystretch}{1}
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\input{exercises.tex}
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\printcollection{banque}
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\end{document}
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\collectexercises{banque}
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\begin{exercise}[subtitle={Malthus}, step={3}, origin={LeLivreScolaire}, topics={Biodiversite Evolution}, tags={Suite, Modélisation}]
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\noindent
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\begin{minipage}{0.49\textwidth}
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@ -13,7 +12,6 @@
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\item En dessinant des représentations graphiques de suites à main levée, expliquer le problème que prédit Malthus à la Grande-Bretagne.
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\item Expliquer comment Verhulst améliore le modèle de Malthus.
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\end{enumerate}
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\end{minipage}
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\hfill
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\begin{minipage}{0.49\textwidth}
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@ -25,9 +23,9 @@
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\end{center}
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\end{bclogo}
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\end{minipage}
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\end{exercise}
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\begin{exercise}[subtitle={Transition Démographique}, step={4}, origin={Créatoin et Le libre scolaire}, topics={Biodiversite Evolution}, tags={Suite, Modélisation}]
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\setlength{\columnseprule}{0pt}
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\begin{multicols}{2}
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\node[roundnode] (centerterm) [right=of leftterme] {\makebox[0.5cm]{}};
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%Lines
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\path[->] (leftterme.east) edge [bend left] node [above] {$\times q$} node [below] {$+t\%$} (centerterm.west);
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\path[->] (leftterme) edge [bend left] node [above] {$\times CM$} node [below] {$+t$} (centerterm);
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\end{tikzpicture}
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\end{minipage}
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\begin{minipage}{0.5\linewidth}
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$q$: coefficient multiplicateur
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$CM$: coefficient multiplicateur
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$t$: taux d'accroissement
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\end{minipage}
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\begin{center}
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$q = 1 + t \qquad \qquad t = q-1$
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$CM = 1 + t \qquad \qquad t = CM-1$
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\bigskip
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avec \qquad t\% $= \frac{t}{100}$ \qquad t \textperthousand $= \frac{t}{1000}$
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\item Compléter le tableau concernant l'étude démographique de l'Afrique du sud.
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\item Identifier la phase 1 puis la phase 2 de la transition démographique de l'Afrique du Sud.
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\item Sachant qu'en 1950, l'Afrique du sud comptait \np{1368300} habitants. Calculer la population en 1955 puis en 2010.
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\item D'après le travail effectué, préparer un bilan sur la transition démographique d'un point de vue mathématique et démographique.
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\item D'après le travail effectué, faire un bilan sur la transition démographique de l'Afrique du sud.
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\end{enumerate}
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\end{exercise}
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\collectexercisesstop{banque}
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Periode,Taux de natalite ,Taux de mortalite ,Taux d'accroissement,Coefficient multiplicateur
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1950-1955,43.3,20.3,,
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1955-1960,42.5,18.1,,
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1960-1965,41.6,16.7,,
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1965-1970,38.2,14.7,,
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1970-1975,37.7,13.1,,
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1975-1980,35.8,11.7,,
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1980-1985,33.9,9.9,,
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1985-1990,31.1,8.6,,
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1990-1995,27.5,8.5,,
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1995-2000,25.1,10.4,,
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2000-2005,24,13.9,,
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2005-2010,21.9,15.2,,
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Periode,Taux de natalite ,Taux de mortalite ,Taux d'accroissement,CoefMult, Population au début
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1950-1955,43.3,20.3,,,
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1955-1960,42.5,18.1,,,
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1960-1965,41.6,16.7,,,
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1965-1970,38.2,14.7,,,
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1970-1975,37.7,13.1,,,
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1975-1980,35.8,11.7,,,
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1980-1985,33.9,9.9,,,
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1985-1990,31.1,8.6,,,
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1990-1995,27.5,8.5,,,
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1995-2000,25.1,10.4,,,
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2000-2005,24,13.9,,,
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2005-2010,21.9,15.2,,,
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