{"id":10,"date":"2023-09-17T11:13:44","date_gmt":"2023-09-17T11:13:44","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e6%8c%87%e6%95%b0%e9%96%a2%e6%95%b0\/"},"modified":"2023-09-17T11:13:44","modified_gmt":"2023-09-17T11:13:44","slug":"%e6%8c%87%e6%95%b0%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e6%8c%87%e6%95%b0%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u6307\u6570\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u6307\u6570\u95a2\u6570\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u6307\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u4e0a\u3067\u8868\u73fe\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u305d\u306e\u3059\u3079\u3066\u306e\u7279\u5fb4\u3068\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u898b\u3066\u3001\u305d\u308c\u3092\u5b8c\u5168\u306b\u7406\u89e3\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u6307\u6570\u95a2\u6570\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3068\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u3044\u3066\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-exponencial\"><\/span>\u6307\u6570\u95a2\u6570\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6307\u6570\u95a2\u6570\u306e\u5b9a\u7fa9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\">\u6570\u5b66\u3067\u306f\u3001<strong>\u6307\u6570\u95a2\u6570\u306f<\/strong>\u3001\u3079\u304d\u4e57\u306e\u6307\u6570\u306b\u72ec\u7acb\u5909\u6570<em>x<\/em>\u3092\u6301\u3064\u95a2\u6570\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-73aa6cf687ce5e8c2f9faf41f5614e53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=a^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u91d1<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u306f\u6b63\u306e\u5b9f\u6570\u3067\u3042\u308a\u30011 \u3068\u306f\u7570\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-funciones-exponenciales\"><\/span>\u6307\u6570\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u95a2\u6570\u306f\u6307\u6570\u95a2\u6570\u306e\u4f8b\u3067\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf0f6145283a443b500a0bfebaec6ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3^{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2ca442ee75f74bd911dd3ab296ac873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=4^{-x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2052342e5fc234eb4428c63b727b4e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\left( \\frac{1}{2} \\right)^x\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"105\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef2b8e1b29b1b10d376713f6fa34fdfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=5^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-las-funciones-exponenciales\"><\/span>\u6307\u6570\u95a2\u6570\u306e\u7279\u5fb4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6307\u6570\u95a2\u6570\u306b\u306f\u6b21\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u6307\u6570\u95a2\u6570\u306e\u5b9a\u7fa9\u57df\u306f\u5b9f\u6570\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6307\u6570\u95a2\u6570\u306f<em>x<\/em>\u306e\u4efb\u610f\u306e\u5024\u306b\u5bfe\u3057\u3066\u5b58\u5728\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91d461485d0f02bb14db6855a3774878_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f=\\mathbff{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li>\u305f\u3060\u3057\u3001\u3053\u306e\u95a2\u6570\u306f\u6b63\u306e\u5024\u306e\u307f\u3092\u53d6\u308b\u305f\u3081\u3001\u6307\u6570\u95a2\u6570\u306e\u7bc4\u56f2\u306f\u6b63\u306e\u5b9f\u6570\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36ed1f92f41441bd0c1d64faa0233a01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Im } f= (0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u3059\u3079\u3066\u306e\u6307\u6570\u95a2\u6570\u306f\u9023\u7d9a\u95a2\u6570\u3067\u3082\u3042\u308a\u3001\u5358\u5c04\u95a2\u6570\u3067\u3082\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u95a2\u6570\u304c\u5909\u63db\u3055\u308c\u306a\u3044\u5834\u5408\u3001\u6307\u6570\u95a2\u6570\u306f\u70b9 (0,1) \u3092\u901a\u904e\u3057\u307e\u3059\u3002\u30bc\u30ed\u3068\u8a55\u4fa1\u3055\u308c\u308b\u95a2\u6570\u306f\u5e38\u306b 1 \u3092\u8fd4\u3059\u305f\u3081\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b49b6b1fa245db9037f372c69f2c1422_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(0)=a^0=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u540c\u69d8\u306b\u3001x=1 \u306b\u304a\u3051\u308b\u6307\u6570\u95a2\u6570\u306e\u5024\u306f\u5e95\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c2f27dba606789a982e3e3c373bda0d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=a^1=a\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d1\u30ef\u30fc\u30d9\u30fc\u30b9\u306a\u3089\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ab31067f7ffbb9fa0478bfb791f6295f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u304c 1 \u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u6307\u6570\u95a2\u6570\u306f\u5897\u52a0\u3057\u307e\u3059\u3002\u4e00\u65b9\u3001\u4fc2\u6570\u304c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u304c 0 \u3068 1 \u306e\u9593\u306e\u7bc4\u56f2\u306b\u3042\u308b\u5834\u5408\u3001\u6307\u6570\u95a2\u6570\u306f\u6e1b\u5c11\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u4e00\u822c\u306b\u3001X \u8ef8\u306f\u6307\u6570\u95a2\u6570\u306e\u6c34\u5e73\u6f38\u8fd1\u7dda\u3067\u3059\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u6307\u6570\u95a2\u6570\u306e\u9006\u95a2\u6570\u304c\u5bfe\u6570\u95a2\u6570\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u3001\u5e95\u304c\u540c\u3058\u3067\u3042\u308c\u3070\u3001\u7dda y=x \u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306b\u306a\u308a\u307e\u3059\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-representar-en-una-grafica-una-funcion-exponencial\"><\/span>\u6307\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u5316\u3059\u308b\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6307\u6570\u95a2\u6570\u306f\u975e\u5e38\u306b\u7c21\u5358\u306b\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u4e0a\u306b\u6307\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u5316\u3059\u308b\u65b9\u6cd5\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u6b21\u306e\u6307\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u306b\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b460d8172e3f8e6633b62ab29e0f220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6307\u6570\u95a2\u6570\u3067\u306f\u3001\u5e38\u306b\u3059\u3079\u3066\u5b9f\u6570\u306b\u306a\u308b\u305f\u3081\u3001\u5b9a\u7fa9\u57df\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd1539b66edeb38040ed80168e1fd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5024\u306e\u8868\u3092\u4f5c\u6210\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u95a2\u6570\u306f\u70b9\u3054\u3068\u306b\u5927\u304d\u304f\u5909\u5316\u3059\u308b\u305f\u3081\u30015 \u3064\u306e\u70b9\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u8a08\u7b97\u3059\u308b\u30dd\u30a4\u30f3\u30c8\u304c\u5897\u3048\u308b\u307b\u3069\u3001\u95a2\u6570\u306e\u8868\u73fe\u306f\u3088\u308a\u6b63\u78ba\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-201\">\n<div class=\"wp-block-column is-layout-flow\">\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e63b3712de818b714fafb781a7aed7b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)=2^0= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57601feaa5d5af3836989b041b20fd1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)=2^1= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c314f7ea92ec93e438d5ca2116be97fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)=2^2= 4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce96f914e1abc10b13488bc390af9501_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)=2^{-1}= 0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"253\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1526d8613884193ce46bf1d8515d8f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)=2^{-2}= 0,25\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-299dcbadf5327b518849f641dd641f34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 1 \\\\ 1 &amp; 2 \\\\ 2 &amp; 4 \\\\ -1 &amp; 0,5 \\\\ -2 &amp; 0,25 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u5024\u306e\u8868\u5185\u306e\u70b9\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u624b\u52d5\u3067\u8a08\u7b97\u3059\u308b\u306e\u304c\u8907\u96d1\u3067\u3042\u308b\u305f\u3081\u3001\u96fb\u5353\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u3001\u30b0\u30e9\u30d5\u4e0a\u306e\u70b9\u3092\u8868\u3057\u307e\u3059<strong>\u3002<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cropped-polynomials-icon-1.png.png\" alt=\"\" class=\"wp-image-249\" width=\"274\" height=\"329\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u6700\u5f8c\u306b\u3001\u70b9\u3092\u7d50\u5408\u3057\u3066\u95a2\u6570\u3092\u62e1\u5f35\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-representation-graphique-d-une-fonction-exponentielle.webp\" alt=\"\u6307\u6570\u95a2\u6570\u3092\u3069\u306e\u3088\u3046\u306b\u8868\u73fe\u307e\u305f\u306f\u30b0\u30e9\u30d5\u5316\u3059\u308b\u304b\" class=\"wp-image-250\" width=\"274\" height=\"326\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u53f3\u5074\u306e\u95a2\u6570\u306f\u7121\u9650\u5927\u307e\u3067\u5897\u5927\u3057\u7d9a\u3051\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u5bfe\u7167\u7684\u306b\u3001\u5de6\u5074\u306e\u95a2\u6570\u306f\u6e1b\u5c11\u3057\u307e\u3059\u304c\u30010 \u306b\u306f\u6c7a\u3057\u3066\u9054\u3057\u307e\u305b\u3093\u30020 \u306b\u975e\u5e38\u306b\u8fd1\u3065\u3044\u3066\u3082\u3001\u6c7a\u3057\u3066\u89e6\u308c\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u7dda y=0 (x \u8ef8) \u304c\u6c34\u5e73\u6f38\u8fd1\u7dda\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-funciones-exponenciales\"><\/span>\u6307\u6570\u95a2\u6570\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u6b21\u306e\u6307\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u306b\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03ffe9b15e527e77fc38e7a090b9086d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= 2^x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u308c\u306f\u6307\u6570\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u308c\u3092\u8868\u3059\u306b\u306f\u3001\u5909\u6570 x \u306b\u5024\u3092\u4e0e\u3048\u308b\u5024\u306e\u30c6\u30fc\u30d6\u30eb\u3092\u4f5c\u6210\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-204\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c782f0c5fc2c9576431a0653e6e954da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)= 2^0+1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a2424217eb051ccbc60bd9c9832cb16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= 2^1+1=3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"229\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46a35a2a78981d594a4599130a5128ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)= 2^2+1=5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fceb9d30fc89075d6f6d367db21aefa0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)= 2^{-1}+1=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"283\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d1d391b6991faa22024aa6164e79fde1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)= 2^{-2}+1=1,25\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"292\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5623433725def7676c75afcfdf23ad6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 2 \\\\ 1 &amp; 3 \\\\ 2 &amp; 5 \\\\ -1 &amp; 1,5 \\\\ -2 &amp; 1,25 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5024\u306e\u8868\u3092\u53d6\u5f97\u3057\u305f\u3089\u3001\u5f97\u3089\u308c\u305f\u70b9\u3092\u30b0\u30e9\u30d5\u4e0a\u306b\u30d7\u30ed\u30c3\u30c8\u3057\u3001\u95a2\u6570\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-etape-par-etape-des-fonctions-exponentielles.webp\" alt=\"\u6307\u6570\u95a2\u6570\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\u6f14\u7fd2\" class=\"wp-image-251\" width=\"301\" height=\"298\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u53f3\u5074\u306e\u95a2\u6570\u306f\u7121\u9650\u5927\u307e\u3067\u5897\u5927\u3057\u7d9a\u3051\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e00\u65b9\u3001\u5de6\u5074\u3067\u306f\u3001\u95a2\u6570\u306f\u6e1b\u5c11\u3057\u307e\u3059\u304c\u30011 \u3092\u8d85\u3048\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5b9f\u969b\u3001\u95a2\u6570\u306f\u53f3\u5074\u306b\u6c34\u5e73\u6f38\u8fd1\u7dda y=1 \u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u3053\u306e\u5834\u5408\u3001\u95a2\u6570\u306b\u5411\u304b\u3063\u3066\u4e0a\u5411\u304d\u306b 1 \u5358\u4f4d\u306e\u5782\u76f4\u79fb\u52d5\u304c\u884c\u308f\u308c\u305f\u305f\u3081\u3001\u6c34\u5e73\u6f38\u8fd1\u7dda\u306f OX \u8ef8\u3067\u306f\u306a\u304f y=1 \u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 2<\/h3>\n<p>\u6b21\u306e\u6307\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u306b\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9a894948fd1963ec5090a0e42d82da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left(\\frac{1}{3}\\right)^x\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"105\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u308c\u306f\u6307\u6570\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u30b0\u30e9\u30d5\u3067\u8868\u3059\u306b\u306f\u3001\u5909\u6570 x \u306b\u5024\u3092\u4e0e\u3048\u308b\u5024\u306e\u30c6\u30fc\u30d6\u30eb\u3092\u4f5c\u6210\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-207\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1ce9dea9f80eeafd40e7e6e13b200ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)= \\left(\\cfrac{1}{3}\\right)^0 = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"228\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-093a357ac3d5530f00f1f69ccd5a0ef4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= \\left(\\cfrac{1}{3}\\right)^1 = 0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"255\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c324f0d99a2076cc1bfb2d38acb9b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)= \\left(\\cfrac{1}{3}\\right)^2 = 0,11\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"254\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e55ea725b4125b1f53dce7b5b42ea633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)= \\left(\\cfrac{1}{3}\\right)^{-1} = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"267\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7f1abd0ebf23e5d165e5d1cfd94afb4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)= \\left(\\cfrac{1}{3}\\right)^{-2} = 9\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"267\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cbf76eff59299da8ebaf3185eef2c654_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 1 \\\\ 1 &amp; 0,33 \\\\ 2 &amp; 0,11 \\\\ -1 &amp; 3 \\\\ -2 &amp; 9 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5024\u306e\u8868\u3092\u53d6\u5f97\u3057\u305f\u3089\u3001\u8a08\u7b97\u3055\u308c\u305f\u70b9\u3092\u30b0\u30e9\u30d5\u4e0a\u306b\u30d7\u30ed\u30c3\u30c8\u3057\u3001\u95a2\u6570\u3092\u63cf\u753b\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/polynomes-px.png\" alt=\"\u6307\u6570\u95a2\u6570\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u305f\" class=\"wp-image-252\" width=\"266\" height=\"454\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5de6\u5074\u306e\u95a2\u6570\u306f\u7121\u9650\u5927\u307e\u3067\u5897\u52a0\u3057\u7d9a\u3051\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e00\u65b9\u3001\u53f3\u5074\u3067\u306f\u3001\u95a2\u6570\u306f\u6e1b\u5c11\u3057\u307e\u3059\u304c\u30010 \u3092\u8d85\u3048\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5b9f\u969b\u3001\u95a2\u6570\u306f y=0 (X \u8ef8) \u3067\u6c34\u5e73\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3092\u6301\u3061\u307e\u3059\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 3<\/h3>\n<p>\u6b21\u306e\u6307\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u306b\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6abae87b33d734a0f0df3fda4b4af143_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left(\\frac{1}{2}\\right)^x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"136\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u308c\u306f\u6307\u6570\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u308c\u3092\u63cf\u753b\u3059\u308b\u306b\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u70b9\u3067\u95a2\u6570\u3092\u8a55\u4fa1\u3059\u308b\u5024\u306e\u30c6\u30fc\u30d6\u30eb\u3092\u4f5c\u6210\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-210\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d86d4d4bb01fc8784c0e389848e82c3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 0 \\ \\longrightarrow \\ f(0)= \\left(\\cfrac{1}{2}\\right)^0+3 = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"259\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa71d27c766686ff32712a8b1767e1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1 \\ \\longrightarrow \\ f(1)= \\left(\\cfrac{1}{2}\\right)^1+3 = 3,5\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"275\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86b1fa3f8b4652a02cc02efc2a75bd80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2 \\ \\longrightarrow \\ f(2)= \\left(\\cfrac{1}{2}\\right)^2+3 = 3,25\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"284\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c27100fdc0eb9ede26c4704ed45d8914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -1 \\ \\longrightarrow \\ f(-1)= \\left(\\cfrac{1}{2}\\right)^{-1}+3 = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"297\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7389ec7cd9ac887cb79f083ba84e92e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= -2 \\ \\longrightarrow \\ f(-2)= \\left(\\cfrac{1}{2}\\right)^{-2}+3 = 7\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"298\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2d6c182e2785f23f50b3b16e4e183157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c|c} x &amp; f(x) \\\\ \\hline 0 &amp; 4 \\\\ 1 &amp; 3,5 \\\\ 2 &amp; 3,25 \\\\ -1 &amp; 5 \\\\ -2 &amp; 7 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"90\" style=\"vertical-align: -62px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6700\u5f8c\u306b\u3001\u53d6\u5f97\u3057\u305f\u70b9\u3092\u30b0\u30e9\u30d5\u4e0a\u306b\u8868\u3057\u3001\u95a2\u6570\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cropped-polynomes-px.png.png\" alt=\"\u6307\u6570\u95a2\u6570\u306e\u554f\u984c\" class=\"wp-image-253\" width=\"305\" height=\"372\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u5de6\u5074\u306e\u95a2\u6570\u306f\u7121\u9650\u306b\u307e\u3067\u7121\u5236\u9650\u306b\u5897\u52a0\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e00\u65b9\u3001\u53f3\u5074\u3067\u306f\u3001\u95a2\u6570\u306f\u6e1b\u5c11\u3057\u307e\u3059\u304c\u30013 \u3092\u8d85\u3048\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5b9f\u969b\u3001\u3053\u306e\u95a2\u6570\u306f y=3 \u3067\u6c34\u5e73\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u3053\u306e\u5834\u5408\u3001\u95a2\u6570\u304c\u5782\u76f4\u65b9\u5411\u306b 3 \u5358\u4f4d\u4e0a\u306b\u79fb\u52d5\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u6c34\u5e73\u65b9\u5411\u306e\u6f38\u8fd1\u7dda\u306f X \u8ef8\u3067\u306f\u306a\u304f y=3 \u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 4<\/h3>\n<p>\u6307\u6570\u95a2\u6570\u306b\u95a2\u3059\u308b\u6b21\u306e\u554f\u984c\u3092\u89e3\u304d\u306a\u3055\u3044\u3002<\/p>\n<ul>\n<li>\u306e\u5024\u3092\u6c7a\u5b9a\u3057\u307e\u3059\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6b21\u306e\u6307\u6570\u95a2\u6570\u304c\u70b9 (2.8) \u3092\u901a\u904e\u3059\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002 <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be030f5f0ee0aada1e1c389763b331d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k\\cdot 2^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"98\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u95a2\u6570\u306f\u70b9 (2,8) \u3092\u901a\u904e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u70b9\u306e<em>x<\/em>\u3068<em>f(x)<\/em>\u306e\u5024\u3092\u95a2\u6570\u306b\u4ee3\u5165\u3057\u3066\u5b9a\u6570<em>k \u306e\u5024\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/em><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bb3d3396e39826e0d6223a79bafe6bf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k\\cdot 2^x \\ \\xrightarrow{x \\ = \\ 2 \\ ; \\ f(x) \\ = \\ 8} \\ 8 = k \\cdot 2^2\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u3001\u7d50\u679c\u3068\u3057\u3066\u5f97\u3089\u308c\u305f\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a345fdf8c61dc26e5092176b51a29e59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8 = k \\cdot 2^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4683f83c268d651c548b98d2320441b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8 = k \\cdot 4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d793900a9bfa50bf89f48216a403e616_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{8}{4} = k\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"41\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34ed53fa864ab9ac888742f196a6453c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{ 2 = k}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 5<\/h3>\n<p>\u6307\u6570\u95a2\u6570\u306b\u95a2\u3059\u308b\u6b21\u306e\u554f\u984c\u3092\u89e3\u304d\u306a\u3055\u3044\u3002<\/p>\n<p>\u30b7\u30ed\u30a2\u30ea\u306e\u96c6\u56e3\u306f\u6b21\u306e\u95a2\u6570\u306b\u5f93\u3063\u3066\u7e41\u6b96\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b41270bdb73979966e8c8e118e76cf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(t)=3^{t+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u91d1<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59d54ba73238a26eb8acae54cb83607e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(t)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"30\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u306f\u30b7\u30ed\u30a2\u30ea\u306e\u6570\u3067\u3042\u308a\u3001<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f55\u304b\u6708\u3082\u7d4c\u3061\u307e\u3057\u305f\u3002<\/p>\n<p> 1\u5e74\u5f8c\u306b\u306f\u4f55\u5339\u306e\u30b7\u30ed\u30a2\u30ea\u304c\u3044\u308b\u3067\u3057\u3087\u3046\u304b\uff1f <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">1 \u5e74\u9593\u306b\u767a\u751f\u3059\u308b\u30b7\u30ed\u30a2\u30ea\u306e\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u95a2\u6570\u306b\u7d4c\u904e\u6642\u9593 (1 \u5e74) \u3092\u4ee3\u5165\u3059\u308b\u3060\u3051\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u95a2\u6570<em>t<\/em>\u306f\u5e74\u3067\u306f\u306a\u304f\u7d4c\u904e\u6708\u3067\u3042\u308b\u305f\u3081\u30011 \u5e74\u306f 12 \u304b\u6708\u3067\u3042\u308b\u305f\u3081\u3001 <em>t<\/em> =12 \u3068\u7f6e\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b41270bdb73979966e8c8e118e76cf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(t)=3^{t+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68f69b244c701ac9238c9939e5d85791_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(12)=3^{12+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-406c5d11e786f4624ffc7834f6b8fe8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(12)=3^{13}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"89\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u96fb\u5353\u3092\u4f7f\u3063\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b44ece2cfd87c845152ec5aa481188fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(12)= 1594323\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3064\u307e\u308a\u30011\u5e74\u5f8c\u306b\u306f1,594,323\u5339\u306e\u30b7\u30ed\u30a2\u30ea\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u6307\u6570\u95a2\u6570\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u6307\u6570\u95a2\u6570\u3092\u30b0\u30e9\u30d5\u4e0a\u3067\u8868\u73fe\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u305d\u306e\u3059\u3079\u3066\u306e\u7279\u5fb4\u3068\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u898b\u3066\u3001\u305d\u308c\u3092\u5b8c\u5168\u306b\u7406\u89e3\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u6307\u6570\u95a2\u6570\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3068\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u3044\u3066\u7df4\u7fd2\u3059\u308b\u3053 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e6%8c%87%e6%95%b0%e9%96%a2%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u6307\u6570\u95a2\u6570<\/span> \u3082\u3063\u3068\u8aad\u3080 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[17],"tags":[],"class_list":["post-10","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized 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