{"id":8067,"date":"2022-11-19T16:32:02","date_gmt":"2022-11-19T15:32:02","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=8067"},"modified":"2025-01-13T16:12:14","modified_gmt":"2025-01-13T15:12:14","slug":"evolution-de-la-population-mondiale","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2022\/11\/19\/evolution-de-la-population-mondiale\/","title":{"rendered":"\u00c9volution de la population mondiale"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Penchons-nous dans cet article sur l&rsquo;\u00e9volution de la population mondiale et \u00e9coutons ce que V\u00e9rino dit sur cette \u00e9volution:<\/p>\n\n\n\n<iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/D6GtSrpx5e4?clip=UgkxZhoJREnkFaG9bLY5ItVy33oXpHl3t1YK&amp;clipt=EJDFAxiUsAQ\" title=\"YouTube video player\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\" width=\"560\" height=\"315\" frameborder=\"0\"><\/iframe>\n\n\n\n<!--more-->\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/11\/19\/evolution-de-la-population-mondiale\/#Evolution_de_la_population_mondiale_resume_en_un_tableau\" >\u00c9volution de la population mondiale: r\u00e9sum\u00e9 en un tableau<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/11\/19\/evolution-de-la-population-mondiale\/#Evolution_de_la_population_mondiale_interpolations\" >\u00c9volution de la population mondiale: interpolations<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/11\/19\/evolution-de-la-population-mondiale\/#Evolution_de_la_population_mondiale_interpolation_polynomiale\" >\u00c9volution de la population mondiale: interpolation polynomiale<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/11\/19\/evolution-de-la-population-mondiale\/#Interpolation_quadratique\" >Interpolation quadratique<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/11\/19\/evolution-de-la-population-mondiale\/#Interpolation_cubique_interpolation_de_Lagrange\" >Interpolation cubique: interpolation de Lagrange<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/11\/19\/evolution-de-la-population-mondiale\/#Interpolation_exponentielle\" >Interpolation exponentielle<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Evolution_de_la_population_mondiale_resume_en_un_tableau\"><\/span>\u00c9volution de la population mondiale: r\u00e9sum\u00e9 en un tableau<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<figure class=\"wp-block-table is-style-stripes\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Ann\u00e9es<\/th><th class=\"has-text-align-center\" data-align=\"center\">Population mondiale (en milliards)<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">1800<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1927<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1975<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2022<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Bien que les nombre de la deuxi\u00e8me colonne forment une suite g\u00e9om\u00e9trique de raison 2, on ne peut pas parler en ces termes car la diff\u00e9rence entre chaque ann\u00e9e n&rsquo;est pas constante.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On peut toutefois entrevoir une \u00e9volution exponentielle \u00e0 l&rsquo;aide du graphique suivant:<\/p>\n\n\n<div class=\"wp-block-image is-style-default\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"235\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-300x235.png\" alt=\"\u00c9volution population mondiale\" class=\"wp-image-8068\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-300x235.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-600x470.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-768x602.png 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image.png 798w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><figcaption class=\"wp-element-caption\">Repr\u00e9sentation des donn\u00e9es de la population mondiale \u00e0 partir de l&rsquo;ann\u00e9e 1800<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Evolution_de_la_population_mondiale_interpolations\"><\/span>\u00c9volution de la population mondiale: interpolations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c0 ce stade, math\u00e9matiquement parl\u00e9, nous avons plusieurs possibilit\u00e9s d&rsquo;interpolations: polynomiale ou exponentielle (on exclut direct l&rsquo;interpolation affine vue la tronche de l&rsquo;\u00e9volution&#8230;).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Evolution_de_la_population_mondiale_interpolation_polynomiale\"><\/span>\u00c9volution de la population mondiale: interpolation polynomiale<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">On pourrait penser que les quatre point du graphique pr\u00e9c\u00e9dent se trouvent (presque) sur une parabole&#8230; ou sur une courbe repr\u00e9sentant un polyn\u00f4me. Le but est donc de trouver une \u00e9quation d&rsquo;une fonction polynomiale passant par ces quatre points.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interpolation_quadratique\"><\/span>Interpolation quadratique<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Dans un premier temps, on se penche sur une \u00e9quation de degr\u00e9 2&#8230; car franchement, les quatre points semblent former une belle parabole non ?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On cherche donc une fonction \\(f\\) telle que \\(f(x)=ax^2+bx+1\\) (\u00ab\u00a01\u00a0\u00bb car la courbe passe par (0;1)).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Il nous faut donc exploiter deux des trois points restants.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>En utilisant les points (127;2) et (175;4), on doit r\u00e9soudre le syst\u00e8me:$$\\begin{cases}127^2a+127b+1=2\\\\175^2a+175b+1=4\\end{cases}$$et on trouve alors:$$a=\\frac{103}{533400},\\quad b=-\\frac{8881}{533400}.$$On obtient alors la courbe suivante:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-2.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"217\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-2-300x217.png\" alt=\"\u00c9volution population mondiale\" class=\"wp-image-8070\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-2-300x217.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-2-600x434.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-2-768x556.png 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-2.png 779w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n<\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>En utilisant les points (127;2) et (222;8), on doit r\u00e9soudre le syst\u00e8me:$$\\begin{cases}127^2a+127b+1=2,222^2a+222b+1=8\\end{cases}$$et on trouve alors:$$a=\\frac{667}{2678430},\\quad b=-\\frac{63619}{2678430}.$$On obtient alors la courbe suivante:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-3.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"206\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-3-300x206.png\" alt=\"\u00c9volution population mondiale\" class=\"wp-image-8071\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-3-300x206.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-3-600x412.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-3.png 768w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n<\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>En utilisant les points (175;4) et (222;8), on obtient:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-4.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"234\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-4-300x234.png\" alt=\"\u00c9volution population mondiale\" class=\"wp-image-8072\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-4-300x234.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-4-600x468.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-4.png 742w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Nous allons donc rejeter l&rsquo;interpolation quadratique car&#8230; trop approximative et surtout&#8230; trop fausse! En effet, entre 1800 et 1927, il n&rsquo;y a pas de baisse de la population mondiale donc ce genre d&rsquo;approximation n&rsquo;est pas coh\u00e9rent.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interpolation_cubique_interpolation_de_Lagrange\"><\/span>Interpolation cubique: interpolation de Lagrange<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">On cherche un polyn\u00f4me passant par TOUS les points. On va donc utiliser le <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Interpolation_lagrangienne\" target=\"_blank\" rel=\"noreferrer noopener\">polyn\u00f4me d&rsquo;interpolation de Lagrange<\/a>: on cherche le polyn\u00f4me P tel que<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Le polyn\u00f4me obtenu est alors:$$P(x)=\\frac{20971 x^3}{17624069400}-\\frac{976673 x^2}{5874689800}+\\frac{86321677 x}{8812034700}+1.$$<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-5.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"220\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-5-300x220.png\" alt=\"\u00c9volution population mondiale\" class=\"wp-image-8073\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-5-300x220.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-5-600x440.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-5-768x563.png 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-5.png 849w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Bien que passant par tous les points, cette interpolation n&rsquo;est pas adapt\u00e9e au contexte. En effet, pourquoi l&rsquo;\u00e9volution suivrait-elle une progression polynomiale cubique ?<\/p>\n\n\n\n<figure class=\"wp-block-pullquote\"><blockquote><p>Sciences sans conscience n&rsquo;est que ruine de l&rsquo;\u00e2me.<\/p><cite>Rabelais<\/cite><\/blockquote><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interpolation_exponentielle\"><\/span>Interpolation exponentielle<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Nous le savons (s\u00fbrement), d\u00e8s lors que nous parlons d&rsquo;\u00e9volution naturelle, il est souvent question d&rsquo;\u00e9volution exponentielle. Il est donc plus naturel de se pencher sur une extrapolation exponentielle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pour cela, nous allons prendre le logarithme n\u00e9p\u00e9rien de la population:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Ann\u00e9es<\/th><th class=\"has-text-align-center\" data-align=\"center\">Logarithme n\u00e9p\u00e9rien de la population mondiale (en milliards)<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">1800<\/td><td class=\"has-text-align-center\" data-align=\"center\">ln(1) = 0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1927<\/td><td class=\"has-text-align-center\" data-align=\"center\">ln(2)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1975<\/td><td class=\"has-text-align-center\" data-align=\"center\">ln(4)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2022<\/td><td class=\"has-text-align-center\" data-align=\"center\">ln(8)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Et nous obtenons le graphique suivant:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-6.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"233\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-6-300x233.png\" alt=\"\u00c9volution population mondiale\" class=\"wp-image-8076\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-6-300x233.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-6-600x465.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-6.png 618w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Maintenant, nous allons faire une approximation affixe (un ajustement lin\u00e9aire). On peut par exemple utiliser Python:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">from numpy import polyfit, corrcoef # pour le calcul des coefficients de la droite de r\u00e9gression\nfrom math import log\n\nx = [ 0, 127, 175, 222 ] \ny = [ 0, log(2), log(4), log(8) ] # consommations (L)\n\ncoef = polyfit( x , y , 1 )\na, b = round(coef[0],3) , round(coef[1],3)\nr = round(corrcoef(x,y)[0][1],3)\n\nprint(f'a = {a}, b = {b}, r = {r}.')<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">a = 0.009, b = -0.144, r = 0.965.<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">On peut ainsi dire que la droite d&rsquo;\u00e9quation \\(y&rsquo; = 0,009x &#8211; 0,144\\) est une approximation du logarithme n\u00e9p\u00e9rien de la population  mondiale.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-7.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"225\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-7-300x225.png\" alt=\"\u00c9volution population mondiale\" class=\"wp-image-8077\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-7-300x225.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-7-600x449.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-7.png 625w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Le coefficient de corr\u00e9lation <em>r<\/em> n&rsquo;est certes pas loin de 1, mais il aurait \u00e9t\u00e9 mieux qu&rsquo;il soit sup\u00e9rieur \u00e0 0,975 pour une corr\u00e9lation mieux adapt\u00e9e&#8230; Mais on va faire avec!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>y<\/em>&lsquo; repr\u00e9sente ln(y) donc:$$y = \\text{e}^{0,009x &#8211; 0,144}.$$<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-8.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"217\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-8-300x217.png\" alt=\"\u00c9volution population mondiale\" class=\"wp-image-8078\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-8-300x217.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-8-600x434.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/11\/image-8.png 710w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Bien qu&rsquo;au premier abord la courbe obtenue paraisse \u00ab\u00a0loin\u00a0\u00bb des points, c&rsquo;est tout de m\u00eame la meilleure approximation possible.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Avec cette approximation, en 2080, la population mondiale serait \u00e9gale (en milliards) \u00e0:$$\\text{e}^{0,009\\times280 &#8211; 0,144}\\approx=10,76.$$<\/p>\n\n\n\n<iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/D6GtSrpx5e4?clip=UgkxU-jlDbz6FkCRBaYZ6peGRfPExe8woWiq&amp;clipt=EI3TBBiHmAU\" title=\"YouTube video player\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\" width=\"560\" height=\"315\" frameborder=\"0\"><\/iframe>\n\n\n\n<p class=\"wp-block-paragraph\">Ainsi, je ne comprends pas comment les sp\u00e9cialistes ont pr\u00e9vu une population mondiale \u00e0 10,4 milliards en 2080&#8230; m\u00eame si on n&rsquo;est pas \u00e0 3 millions pr\u00e8s \u00e0 cette \u00e9chelle&#8230;<\/p>\n\n\n\n<pre class=\"wp-block-verse\"><strong>La cha\u00eene Youtube de V\u00e9rino:<\/strong> <a href=\"https:\/\/www.youtube.com\/@Verinaze\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/www.youtube.com\/@Verinaze<\/a><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Penchons-nous dans cet article sur l&rsquo;\u00e9volution de la population mondiale et \u00e9coutons ce que V\u00e9rino dit sur cette \u00e9volution:<\/p>\n","protected":false},"author":1,"featured_media":8079,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[374,373,376,372],"class_list":["post-8067","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematiques","tag-ajustement-lineaire","tag-interpolation","tag-polynome-de-lagrange","tag-statistiques"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - 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