{"id":248029,"date":"2025-07-08T05:39:51","date_gmt":"2025-07-08T05:39:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248029"},"modified":"2025-07-08T05:39:53","modified_gmt":"2025-07-08T05:39:53","slug":"write-the-equation-of-the-model-for-the-citys-population-decay-in-terms-of-t","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/write-the-equation-of-the-model-for-the-citys-population-decay-in-terms-of-t\/","title":{"rendered":"Write the equation of the model for the city&#8217;s population decay in terms of t"},"content":{"rendered":"\n<p>Write the equation of the model for the city&#8217;s population decay in terms of t<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To model the population decay of a city over time, we can use the general exponential decay equation:P(t)=P0\u22c5e\u2212ktP(t) = P_0 \\cdot e^{-kt}P(t)=P0\u200b\u22c5e\u2212kt<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(t)P(t)P(t) is the population at time ttt,<\/li>\n\n\n\n<li>P0P_0P0\u200b is the initial population at time t=0t = 0t=0,<\/li>\n\n\n\n<li>kkk is the decay constant (a positive number for decay),<\/li>\n\n\n\n<li>ttt is the time variable, typically in years, months, or another time unit.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>In this equation, the population decreases exponentially over time. The factor e\u2212kte^{-kt}e\u2212kt represents the rate of decay. Exponential decay is characterized by a constant percentage reduction over each time interval. This means that the longer the time passes, the smaller the population becomes, following a consistent pattern.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Initial Population<\/strong>: The value P0P_0P0\u200b represents the initial population of the city at the beginning of the time period. It is the population at t=0t = 0t=0, and it determines the starting value for the model.<\/li>\n\n\n\n<li><strong>Decay Constant<\/strong>: The decay constant kkk determines how quickly the population decreases. The larger the value of kkk, the faster the decay. For example, if k=0.05k = 0.05k=0.05, the population decays at a rate of 5% per unit of time. A smaller kkk means a slower rate of decay.<\/li>\n\n\n\n<li><strong>Time Variable<\/strong>: The time variable ttt represents the time that has passed since the initial population measurement. As ttt increases, the population P(t)P(t)P(t) decreases exponentially.<\/li>\n<\/ol>\n\n\n\n<p>This model assumes that the city&#8217;s population decreases without external factors like immigration or significant changes in birth rates. It reflects situations where a population declines at a steady, predictable rate.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-1082.jpeg\" alt=\"\" class=\"wp-image-248030\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Write the equation of the model for the city&#8217;s population decay in terms of t The Correct Answer and Explanation is: To model the population decay of a city over time, we can use the general exponential decay equation:P(t)=P0\u22c5e\u2212ktP(t) = P_0 \\cdot e^{-kt}P(t)=P0\u200b\u22c5e\u2212kt Where: Explanation: In this equation, the population decreases exponentially over time. The [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-248029","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248029","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=248029"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248029\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248029"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248029"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248029"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}