{"id":248041,"date":"2025-07-08T05:49:34","date_gmt":"2025-07-08T05:49:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248041"},"modified":"2025-07-08T05:49:36","modified_gmt":"2025-07-08T05:49:36","slug":"write-the-equation-of-the-model-for-the-citys-population-decay-in-terms-of-t-2","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-2\/","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-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The equation of a population decay model is typically written in the form:P(t)=P0e\u2212ktP(t) = P_0 e^{-kt}P(t)=P0\u200be\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 (which determines the rate of population decrease),<\/li>\n\n\n\n<li>ttt is the time that has passed.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The equation models exponential decay, which is a common way to represent populations that decrease over time (such as in the case of species extinction, urban depopulation, etc.).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The initial population P0P_0P0\u200b represents the population at time t=0t = 0t=0, when the decay process starts. This is the point at which the population is at its maximum before any decay has occurred.<\/li>\n\n\n\n<li>The decay constant kkk is a positive number that describes the rate at which the population decreases. A larger value of kkk means the population decreases more rapidly.<\/li>\n\n\n\n<li>The exponential function e\u2212kte^{-kt}e\u2212kt shows how the population declines over time. As ttt increases, the exponent becomes more negative, causing P(t)P(t)P(t) to decrease over time.<\/li>\n\n\n\n<li>The time variable ttt typically represents the amount of time that has passed since the start of the observation.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Example:<\/h3>\n\n\n\n<p>If the population of a city starts at 100,000 people and the population decreases at a rate of 2% per year, the decay constant kkk would be 0.020.020.02. The population model would then be:P(t)=100000e\u22120.02tP(t) = 100000 e^{-0.02t}P(t)=100000e\u22120.02t<\/p>\n\n\n\n<p>This means that after 1 year, the population would be approximately P(1)=100000e\u22120.02\u00d71\u224898,000P(1) = 100000 e^{-0.02 \\times 1} \\approx 98,000P(1)=100000e\u22120.02\u00d71\u224898,000, showing a decrease of 2%. The exponential decay ensures the population will continue to decrease indefinitely, though the rate of decay slows down as time passes.<\/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-banner5-1085.jpeg\" alt=\"\" class=\"wp-image-248042\"\/><\/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: The equation of a population decay model is typically written in the form:P(t)=P0e\u2212ktP(t) = P_0 e^{-kt}P(t)=P0\u200be\u2212kt Where: Explanation: The equation models exponential decay, which is a common way to represent populations that decrease over [&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-248041","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248041","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=248041"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248041\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}