{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![En tête general](img/En_tete_general.png)\n",
"\n",
"\n",
"*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n",
"\n",
" Pour exécuter une saisie Python, sélectionner la cellule et valider avec SHIFT+Entrée.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Le Banquier et le Savetier (corrigé) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![Illustration Banquier Savetier](img/Banquier_Savetier.png)\n",
"\n",
"Le banquier, M Malin, rencontre le savetier, M Circonspect.\n",
"\n",
"M Circonspect lui propose un marché :\n",
"« Ce mois ci, qui compte 31 jours, je te propose le marché suivant :\n",
"Je te verse :\t20 000 € le 0ème jour (aujourd’hui), \n",
"\t\t30 000 € le 1er jour, \n",
"\t\t40 000 € le 2ème jour\n",
"\t\t… etc… en ajoutant 10 000€ chaque jour.\n",
"En échange, tu me donnes :\n",
"\t\t1 € le 0ème jour, \n",
"\t\t2 € le 1er jour, \n",
"\t\t4 € le 2ème jour, \n",
"\t\t8 € le 3ème jour,\n",
"\t\t… etc… en doublant à chaque fois ce que tu m’as donné la veille. \n",
"L’engagement dure sur un mois, es-tu prêt à signer le contrat ? ».\n",
"\n",
"« Quel imbécile ! » se dit M Malin, qui accepta sans sourciller le contrat.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__1. Expliquer ce que renvoient les fonctions ci-dessous.__"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"def C(n):\n",
" a=20000\n",
" for k in range(n):\n",
" a = a+10000\n",
" return a\n",
"\n",
"def cherche():\n",
" n=0\n",
" while C(n)<150000:\n",
" n=n+1\n",
" return n"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"(160000, 13)"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"C(14) , cherche()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__2- Écrire une fonction M donnant la somme versée par M Malin le n ème jour.__"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"def M(n):\n",
" a=1\n",
" for k in range(n):\n",
" a = a*2\n",
" return a"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"16384"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M(14)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__3- Écrire une fonction donnant le jour à partir duquel M Malin verse plus que M Circonspect.__"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"def Comp(C,M):\n",
" n=0\n",
" while C(n)>M(n):\n",
" n=n+1\n",
" return n"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"18"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Comp(C,M)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__4- Écrire une fonction donnant la somme versée en tout par M Circonspect le n ème jour.__"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"# Ecrire la fonction\n",
"def somme(C,n):\n",
" S=0\n",
" for k in range(n+1):\n",
" S=S+C(k)\n",
" return S"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1350000"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Tester la fonction\n",
"somme(C,14)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*__Répondre aux questions 5,6,7 en utilisant/modifiant les fonctions précédentes.__*\n",
"\n",
"\n",
" \n",
"__5- Déterminer le premier jour au bout duquel M Circonspect versera plus de 125000 €.__\n",
"\n",
"\n",
" \n",
"__6- Déterminer le premier jour au bout duquel M Malin versera plus de 180000 €.__\n",
"\n",
"\n",
" \n",
"__7- Déterminer la somme versée en tout par M Malin le 15 ème jour.__"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(11, 18, 65535)"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# On peut adapter la fonction cherche:\n",
"\n",
"def cherche2(C,seuil):\n",
" n=0\n",
" while C(n) Alcuin (au centre) (735-804) a écrit un recueil d'exercices mathématiques, où apparaissait l'équivalent de la notion de suite géométrique de raison 2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n"
]
}
],
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"celltoolbar": "Raw Cell Format",
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