{"id":10,"date":"2023-09-17T11:13:44","date_gmt":"2023-09-17T11:13:44","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%8c%87%e6%95%b0%e5%87%bd%e6%95%b0\/"},"modified":"2023-09-17T11:13:44","modified_gmt":"2023-09-17T11:13:44","slug":"%e6%8c%87%e6%95%b0%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%8c%87%e6%95%b0%e5%87%bd%e6%95%b0\/","title":{"rendered":"\u6307\u6570\u51fd\u6570"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u6307\u6570\u51fd\u6570\u4ee5\u53ca\u5982\u4f55\u5728\u56fe\u5f62\u4e0a\u8868\u793a\u6307\u6570\u51fd\u6570\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u770b\u5230\u5b83\u7684\u6240\u6709\u7279\u6027\u548c\u51e0\u4e2a\u793a\u4f8b\u4ee5\u5145\u5206\u7406\u89e3\u5b83\u3002\u6700\u540e\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u6307\u6570\u51fd\u6570\u7684\u7ec3\u4e60\u548c\u9010\u6b65\u89e3\u51b3\u7684\u95ee\u9898\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-exponencial\"><\/span>\u4ec0\u4e48\u662f\u6307\u6570\u51fd\u6570\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6307\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a <\/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\">\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u6307\u6570\u51fd\u6570<\/strong>\u662f\u81ea\u53d8\u91cf<em>x<\/em>\u4e3a\u5e42\u6307\u6570\u7684\u51fd\u6570\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u4eec\u5982\u4e0b\uff1a<\/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\u5b50<\/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>\u662f\u4e00\u4e2a\u4e0d\u540c\u4e8e 1 \u7684\u6b63\u5b9e\u6570\u3002 <\/p>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-funciones-exponenciales\"><\/span>\u6307\u6570\u51fd\u6570\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4ee5\u4e0b\u51fd\u6570\u662f\u6307\u6570\u51fd\u6570\u7684\u793a\u4f8b\uff1a <\/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\u51fd\u6570\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6307\u6570\u51fd\u6570\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a<\/p>\n<ul>\n<li>\u6307\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u7531\u5b9e\u6570\u7ec4\u6210\uff0c\u6362\u53e5\u8bdd\u8bf4\uff0c\u5bf9\u4e8e\u4efb\u4f55<em>x<\/em>\u503c\u90fd\u5b58\u5728\u6307\u6570\u51fd\u6570\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>\u7136\u800c\uff0c\u8be5\u51fd\u6570\u53ea\u53d6\u6b63\u503c\uff0c\u56e0\u6b64\u6307\u6570\u51fd\u6570\u7684\u8303\u56f4\u7531\u6b63\u5b9e\u6570\u7ec4\u6210\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>\u6bcf\u4e2a\u6307\u6570\u51fd\u6570\u65e2\u662f\u8fde\u7eed\u51fd\u6570\u53c8\u662f\u5355\u5c04\u51fd\u6570\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u5982\u679c\u51fd\u6570\u4e0d\u5e73\u79fb\uff0c\u5219\u4efb\u4f55\u6307\u6570\u51fd\u6570\u90fd\u4f1a\u7ecf\u8fc7\u70b9 (0,1)\u3002\u56e0\u4e3a\u8ba1\u7b97\u4e3a\u96f6\u7684\u51fd\u6570\u603b\u662f\u7ed9\u51fa\u4e00\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>\u7c7b\u4f3c\u5730\uff0c\u6307\u6570\u51fd\u6570\u5728 x=1 \u5904\u7684\u503c\u7b49\u4e8e\u5e95\u6570\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>\u5982\u679c\u7535\u6e90\u5e95\u5ea7\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>\u5927\u4e8e1\uff0c\u6307\u6570\u51fd\u6570\u9012\u589e\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u7cfb\u6570<\/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>\u5728 0 \u548c 1 \u4e4b\u95f4\uff0c\u6307\u6570\u51fd\u6570\u662f\u9012\u51cf\u7684\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u4e00\u822c\u6765\u8bf4\uff0cx \u8f74\u662f\u6307\u6570\u51fd\u6570\u7684\u6c34\u5e73\u6e10\u8fd1\u7ebf\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u6307\u6570\u51fd\u6570\u7684\u53cd\u51fd\u6570\u662f\u5bf9\u6570\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6307\u6570\u51fd\u6570\u548c\u5bf9\u6570\u51fd\u6570\u5177\u6709\u76f8\u540c\u7684\u5e95\uff0c\u5219\u5b83\u4eec\u7684\u56fe\u5f62\u5173\u4e8e\u76f4\u7ebf y=x \u5bf9\u79f0\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>\u5982\u4f55\u7ed8\u5236\u6307\u6570\u51fd\u6570\u7684\u56fe\u5f62<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6307\u6570\u51fd\u6570\u7684\u8868\u793a\u975e\u5e38\u7b80\u5355\u3002\u56e0\u6b64\uff0c\u8ba9\u6211\u4eec\u901a\u8fc7\u793a\u4f8b\u4e86\u89e3\u5982\u4f55\u5728\u56fe\u8868\u4e0a\u7ed8\u5236\u6307\u6570\u51fd\u6570\u3002<\/p>\n<ul>\n<li>\u5728\u56fe\u4e0a\u7ed8\u5236\u4ee5\u4e0b\u6307\u6570\u51fd\u6570\uff1a<\/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>\u5728\u6307\u6570\u51fd\u6570\u4e2d\uff0c\u4e0d\u9700\u8981\u8ba1\u7b97\u5b9a\u4e49\u57df\uff0c\u56e0\u4e3a\u5b83\u4eec\u59cb\u7ec8\u90fd\u662f\u5b9e\u6570\uff1a<\/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>\u56e0\u6b64\uff0c\u5236\u5b9a\u4ef7\u503c\u8868\u5c31\u8db3\u591f\u4e86\u3002\u7531\u4e8e\u8fd9\u4e9b\u7c7b\u578b\u7684\u51fd\u6570\u4ece\u4e00\u4e2a\u70b9\u5230\u53e6\u4e00\u4e2a\u70b9\u53d8\u5316\u5f88\u5927\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97 5 \u4e2a\u70b9\u3002\u4f46\u662f\u6211\u4eec\u8ba1\u7b97\u7684\u70b9\u8d8a\u591a\uff0c\u51fd\u6570\u7684\u8868\u793a\u5c31\u8d8a\u7cbe\u786e\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>\u6211\u4eec\u5efa\u8bae\u4f7f\u7528\u8ba1\u7b97\u5668\u6765\u67e5\u627e\u6570\u503c\u8868\u4e2d\u7684\u70b9\uff0c\u56e0\u4e3a\u624b\u52a8\u8ba1\u7b97\u8fd9\u4e9b\u70b9\u5f88\u590d\u6742\u3002<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5728\u56fe\u8868\u4e0a\u8868\u793a\u70b9<strong>\uff1a<\/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\u540e\uff0c\u6211\u4eec\u8fde\u63a5\u70b9\u5e76\u6269\u5c55\u51fd\u6570\uff1a <\/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=\"\u5982\u4f55\u8868\u793a\u6216\u7ed8\u5236\u6307\u6570\u51fd\u6570\u7684\u56fe\u8868\" class=\"wp-image-250\" width=\"274\" height=\"326\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u8bf7\u6ce8\u610f\uff0c\u53f3\u4fa7\u7684\u51fd\u6570\u7ee7\u7eed\u589e\u957f\u76f4\u81f3\u65e0\u7a77\u5927\u3002<\/p>\n<p>\u76f8\u53cd\uff0c\u5de6\u8fb9\u7684\u51fd\u6570\u51cf\u5c11\u4f46\u6c38\u8fdc\u4e0d\u4f1a\u8fbe\u5230 0\u3002\u5373\u4f7f\u5b83\u975e\u5e38\u63a5\u8fd1\u5b83\uff0c\u5b83\u4e5f\u6c38\u8fdc\u4e0d\u4f1a\u89e6\u53ca\u5b83\u3002\u8fd9\u610f\u5473\u7740\u7ebf y=0\uff08x \u8f74\uff09\u662f\u6c34\u5e73\u6e10\u8fd1\u7ebf\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-funciones-exponenciales\"><\/span>\u89e3\u7b54\u4e86\u6307\u6570\u51fd\u6570\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u7ed8\u5236\u4ee5\u4e0b\u6307\u6570\u51fd\u6570\u7684\u56fe\u5f62\uff1a <\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5b83\u662f\u4e00\u4e2a\u6307\u6570\u51fd\u6570\uff0c\u56e0\u6b64\u8981\u8868\u793a\u5b83\uff0c\u60a8\u5fc5\u987b\u521b\u5efa\u4e00\u4e2a\u503c\u8868\uff0c\u4e3a\u53d8\u91cf x \u8d4b\u4e88\u503c\uff1a <\/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\">\u4e00\u65e6\u6211\u4eec\u6709\u4e86\u6570\u503c\u8868\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5728\u56fe\u8868\u4e0a\u7ed8\u5236\u83b7\u5f97\u7684\u70b9\u5e76\u7ed8\u5236\u51fd\u6570\uff1a <\/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=\"\u9010\u6b65\u89e3\u51b3\u6307\u6570\u51fd\u6570\u7684\u7ec3\u4e60\" class=\"wp-image-251\" width=\"301\" height=\"298\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u8bf7\u6ce8\u610f\uff0c\u53f3\u4fa7\u7684\u51fd\u6570\u7ee7\u7eed\u589e\u957f\u76f4\u81f3\u65e0\u7a77\u5927\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u5de6\u4fa7\uff0c\u51fd\u6570\u51cf\u5c0f\u4f46\u4ece\u672a\u8d85\u8fc7 1\u3002\u5b9e\u9645\u4e0a\uff0c\u51fd\u6570\u5728\u53f3\u4fa7 y=1 \u5904\u6709\u4e00\u6761\u6c34\u5e73\u6e10\u8fd1\u7ebf\u3002<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6c34\u5e73\u6e10\u8fd1\u7ebf\u4f4d\u4e8e y=1 \u800c\u4e0d\u662f OX \u8f74\uff0c\u56e0\u4e3a\u5df2\u7ecf\u671d\u7740\u51fd\u6570\u5411\u4e0a\u5782\u76f4\u5e73\u79fb\u4e86\u4e00\u4e2a\u5355\u4f4d\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u5728\u56fe\u4e0a\u7ed8\u5236\u4ee5\u4e0b\u6307\u6570\u51fd\u6570\uff1a <\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5b83\u662f\u4e00\u4e2a\u6307\u6570\u51fd\u6570\uff0c\u56e0\u6b64\u8981\u4ee5\u56fe\u5f62\u65b9\u5f0f\u8868\u793a\u5b83\uff0c\u60a8\u5fc5\u987b\u6784\u9020\u4e00\u4e2a\u503c\u8868\uff0c\u4e3a\u53d8\u91cf x \u8d4b\u4e88\u503c\uff1a <\/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\">\u4e00\u65e6\u6211\u4eec\u6709\u4e86\u6570\u503c\u8868\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5728\u56fe\u8868\u4e0a\u7ed8\u5236\u8ba1\u7b97\u70b9\u5e76\u7ed8\u5236\u51fd\u6570\uff1a <\/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=\"\u89e3\u51b3\u6307\u6570\u51fd\u6570\u7ec3\u4e60\" class=\"wp-image-252\" width=\"266\" height=\"454\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u8bf7\u6ce8\u610f\uff0c\u5de6\u4fa7\u7684\u51fd\u6570\u7ee7\u7eed\u589e\u957f\u76f4\u81f3\u65e0\u7a77\u5927\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u53f3\u4fa7\uff0c\u51fd\u6570\u51cf\u5c0f\u4f46\u4ece\u672a\u8d85\u8fc7 0\u3002\u5b9e\u9645\u4e0a\uff0c\u51fd\u6570\u5728 y=0\uff08X \u8f74\uff09\u5904\u6709\u4e00\u6761\u6c34\u5e73\u6e10\u8fd1\u7ebf\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u5728\u56fe\u4e0a\u7ed8\u5236\u4ee5\u4e0b\u6307\u6570\u51fd\u6570\uff1a <\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5b83\u662f\u4e00\u4e2a\u6307\u6570\u51fd\u6570\uff0c\u56e0\u6b64\u8981\u7ed8\u5236\u5b83\uff0c\u60a8\u5fc5\u987b\u521b\u5efa\u4e00\u4e2a\u503c\u8868\uff0c\u5728\u51e0\u4e2a\u70b9\u4e0a\u8bc4\u4f30\u8be5\u51fd\u6570\uff1a <\/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\u540e\uff0c\u6211\u4eec\u5c06\u83b7\u5f97\u7684\u70b9\u8868\u793a\u5728\u56fe\u4e0a\u5e76\u7ed8\u5236\u51fd\u6570\uff1a <\/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\u51fd\u6570\u95ee\u9898\" class=\"wp-image-253\" width=\"305\" height=\"372\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u8bf7\u6ce8\u610f\uff0c\u5de6\u8fb9\u7684\u51fd\u6570\u65e0\u9650\u589e\u957f\u5230\u65e0\u7a77\u5927\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u53f3\u4fa7\uff0c\u51fd\u6570\u51cf\u5c0f\u4f46\u4ece\u672a\u8d85\u8fc7 3\u3002\u5b9e\u9645\u4e0a\uff0c\u51fd\u6570\u5728 y=3 \u5904\u6709\u6c34\u5e73\u6e10\u8fd1\u7ebf\u3002<\/p>\n<p class=\"has-text-align-left\">\u5728\u672c\u4f8b\u4e2d\uff0c\u6c34\u5e73\u6e10\u8fd1\u7ebf\u4f4d\u4e8e y=3 \u800c\u4e0d\u662f X \u8f74\uff0c\u56e0\u4e3a\u51fd\u6570\u5df2\u5782\u76f4\u5411\u4e0a\u79fb\u52a8\u4e86\u4e09\u4e2a\u5355\u4f4d\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u89e3\u51b3\u4ee5\u4e0b\u6709\u5173\u6307\u6570\u51fd\u6570\u7684\u95ee\u9898\u3002<\/p>\n<ul>\n<li>\u786e\u5b9a \u7684\u503c\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>\u4f7f\u5f97\u4e0b\u4e00\u4e2a\u6307\u6570\u51fd\u6570\u901a\u8fc7\u70b9(2.8)\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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u51fd\u6570\u5fc5\u987b\u7ecf\u8fc7\u70b9(2,8)\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5c06\u8be5\u70b9\u7684<em>x<\/em>\u548c<em>f(x)<\/em>\u7684\u503c\u4ee3\u5165\u51fd\u6570\u4e2d\u6c42\u5f97\u5e38\u6570<em>k\u7684\u503c\uff1a<\/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\">\u73b0\u5728\u6211\u4eec\u6c42\u89e3\u6240\u5f97\u65b9\u7a0b\uff1a <\/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\">\u7ec3\u4e605<\/h3>\n<p>\u89e3\u51b3\u4ee5\u4e0b\u6709\u5173\u6307\u6570\u51fd\u6570\u7684\u95ee\u9898\u3002<\/p>\n<p>\u767d\u8681\u79cd\u7fa4\u6839\u636e\u4ee5\u4e0b\u529f\u80fd\u8fdb\u884c\u7e41\u6b96\uff1a<\/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\u5b50<\/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>\u662f\u767d\u8681\u7684\u6570\u91cf\uff0c<\/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>\u65f6\u95f4\u5df2\u7ecf\u8fc7\u53bb\u51e0\u4e2a\u6708\u4e86\u3002<\/p>\n<p> 1\u5e74\u540e\u4f1a\u6709\u591a\u5c11\u767d\u8681\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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u4e00\u5e74\u5185\u767d\u8681\u7684\u6570\u91cf\uff0c\u53ea\u9700\u5c06\u7ecf\u8fc7\u7684\u65f6\u95f4\uff081 \u5e74\uff09\u4ee3\u5165\u51fd\u6570\u5373\u53ef\u3002\u4f46\u7531\u4e8e\u51fd\u6570<em>t<\/em>\u662f\u7ecf\u8fc7\u7684\u6708\u4efd\u800c\u4e0d\u662f\u5e74\u4efd\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u5c06<em>t<\/em> =12\uff0c\u56e0\u4e3a\u4e00\u5e74\u6709 12 \u4e2a\u6708\uff1a <\/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\">\u6211\u4eec\u7528\u8ba1\u7b97\u5668\u6c42\u89e3\uff1a<\/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\">\u6240\u4ee5\u4e00\u5e74\u540e\u5c06\u4f1a\u6709 1,594,323 \u53ea\u767d\u8681\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u6307\u6570\u51fd\u6570\u4ee5\u53ca\u5982\u4f55\u5728\u56fe\u5f62\u4e0a\u8868\u793a\u6307\u6570\u51fd\u6570\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u770b\u5230\u5b83\u7684\u6240\u6709\u7279\u6027\u548c\u51e0\u4e2a\u793a\u4f8b\u4ee5\u5145\u5206\u7406\u89e3 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%8c%87%e6%95%b0%e5%87%bd%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u6307\u6570\u51fd\u6570<\/span> \u67e5\u770b\u5168\u6587 &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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