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+\xsimsetup{ + step=3, +} + +\begin{document} +\input{exercises.tex} +\printcollection{banque} +\vfill + +\printcollection{banque} +\vfill + +\end{document} diff --git a/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex b/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex index 72191bf..d3de511 100644 --- a/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex @@ -73,4 +73,49 @@ \end{minipage} \end{exercise} +\begin{exercise}[subtitle={Simplifications}, step={3}, origin={Création}, topics={Prolongement géométrique vers exponentiel}, tags={exponentiel, suite, programmation}] + Mettre les quantités suivantes sous la forme $a\times b^n$. + \begin{multicols}{3} + \begin{enumerate} + \item $A=5^2\times 5^{-3}\times 5^5$ + \item $B=\dfrac{1,5^3}{1,5^6}$ + \item $C=(2^2)^5 \times 2^{-3}$ + \item $D= 2^4 - (2^2)^2$ + \item $E=2\times10^3 + 10^3$ + \item $F=1,5^{10} + 3(1,5^2)^5$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Réduction}, step={3}, origin={Création}, topics={Prolongement géométrique vers exponentiel}, tags={exponentiel, suite, programmation}] + Réduire les expressions suivantes pour obtenir des fonctions et reconnaître les fonctions puissances. + \begin{multicols}{3} + \begin{enumerate} + \item $A=10^x + 10^x + 10^x$ + \item $B=(2^x)^3$ + \item $C=3\times 2^x + 10 \times 2^x$ + \item $D=x\times 5^x + 2 \times 5^x$ + \item $E=(x+1)\times10^x + 2x \times 10^x$ + \item $F=2^2x\times 2^{x -1}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Concentration dans le sange}, step={3}, origin={Création}, topics={Prolongement géométrique vers exponentiel}, tags={exponentiel, suite, programmation}] + On injecte dans le sang d'un patient une dose de 4mg d'un médicament. On suppose que le médicament se répartit instantanément dans le sang. + + On note $t$ le temps écoulé en minutes depuis l'injection et on modélise la quantité $Q(t)$ (en mg) de médicament présent dans le sang par la fonction définie sur $\intFO{0}{+\infty}$. + \[ + Q(t) = 4\times0.85^t + \] + \begin{enumerate} + \item Calculer et interpréter $Q(0)$, $Q(10)$, $Q(5,5)$. + \item Quel est le sens de variation de $Q$. Interpréter ce résultat. + \item Quelle est la quantité de médicament dans le sang 1h30 après l'injection? + \item Le médicament n'est plus efficace si sa quantité est inférieur à 1mg. Au bout de combien de temps va-t-il devenir inefficace? + \end{enumerate} +\end{exercise} + + + \collectexercisesstop{banque}