{"id":156314,"date":"2022-03-26T01:37:09","date_gmt":"2022-03-25T20:07:09","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/exponential-growth-explanation-graph-equation-decay-solved-example-and-faqs\/"},"modified":"2025-06-23T17:04:12","modified_gmt":"2025-06-23T11:34:12","slug":"exponential-growth-explanation-graph-equation-decay-solved-example-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/exponential-growth\/","title":{"rendered":"Exponential Growth &#8211; Explanation, Graph, Equation, Decay, Solved Example, and FAQs"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-growth\/#What_is_Exponential_Growth\" title=\"What is Exponential Growth?\">What is Exponential Growth?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-growth\/#Exponential_Decay\" title=\"Exponential Decay\">Exponential Decay<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-growth\/#Exponential_Decay_Formula\" title=\"Exponential Decay Formula\">Exponential Decay Formula<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Exponential_Growth\"><\/span>What is Exponential Growth?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In mathematics and physics, exponential growth is a type of growth in which the proportional rate of increase is proportional to the current size of the object. In other words, the size of the object is multiplied by the growth rate each time the object is measured. Exponential Growth &#8211; Explanation Graph Equation Decay .<\/p>\n<p>For example, if an object is measured to be 2 centimeters long, and the growth rate is 1 centimeter per day, then the object will be 4 centimeters long after one day, 8 centimeters long after two days, and so on.<\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"HMxU9HiyNI\"><p><a href=\"https:\/\/infinitylearn.com\/surge\/iit-jee\">JEE Exam 2025, JEE Main 2025 Application Form (OUT)<\/a><\/p><\/blockquote>\n<p><iframe class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; clip: rect(1px, 1px, 1px, 1px);\" title=\"&#8220;JEE Exam 2025, JEE Main 2025 Application Form (OUT)&#8221; &#8212; Infinity Learn by Sri Chaitanya\" src=\"https:\/\/infinitylearn.com\/surge\/iit-jee\/embed\/#?secret=HMxU9HiyNI\" data-secret=\"HMxU9HiyNI\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>\\[N=N_0e^{rt}\\]\n<p>where<\/p>\n<p><strong>N is the population or quantity at time t<\/strong><\/p>\n<p><strong>N 0 is the initial population or quantity<\/strong><\/p>\n<p><strong>r is the growth rate<\/strong><\/p>\n<p><strong>t is the time in years<\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Exponential_Decay\"><\/span>Exponential Decay<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In exponential decay, the decay rate is proportional to the current amount of the substance.<\/p>\n<p>$\\frac{dN}{dt} = k N$<\/p>\n<p>Where<\/p>\n<p>$dN$ = the change in the amount of the substance over time, in units of the substance<\/p>\n<p>$dt$ = the change in time, in units of time<\/p>\n<p>$k$ = the decay rate, in units of the substance per unit time<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Exponential_Decay_Formula\"><\/span>Exponential Decay Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The exponential decay formula is a mathematical equation that describes the rate at which a quantity decays over time. The equation is:<\/p>\n<ul>\n<li>The quantity &#8220;N&#8221; represents the amount of the substance at time &#8220;t&#8221; and &#8220;k&#8221; is the decay constant.<\/li>\n<li>The decay constant is a measure of how quickly the substance decays and is typically expressed in units of inverse time (e.g. seconds-1).<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>What is Exponential Growth? In mathematics and physics, exponential growth is a type of growth in which the proportional rate [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Exponential Growth - Explanation Graph","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Exponential Growth - Explanation Graph Equation Decay in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/exponential-growth\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exponential Growth - Explanation, Graph, Equation, Decay, Solved Example, and FAQs - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Exponential Growth - Explanation Graph Equation Decay in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/exponential-growth\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Exponential Growth - 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