{"id":271677,"date":"2025-07-26T06:13:01","date_gmt":"2025-07-26T06:13:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271677"},"modified":"2025-07-26T06:13:03","modified_gmt":"2025-07-26T06:13:03","slug":"the-population-of-a-town-is-2500-and-is-decreasing-at-a-rate-of-3-5-per-year","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/26\/the-population-of-a-town-is-2500-and-is-decreasing-at-a-rate-of-3-5-per-year\/","title":{"rendered":"The population of a town is 2500 and is decreasing at a rate of 3.5% per year."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-739.png\" alt=\"\" class=\"wp-image-271678\"\/><\/figure>\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 population of the town after 5 years will be approximately&nbsp;<strong>2092<\/strong>.<\/p>\n\n\n\n<p><strong>Explanation<\/strong><\/p>\n\n\n\n<p>This problem involves exponential decay, which describes how a quantity decreases at a rate proportional to its current value. To solve this, we use the exponential decay formula, which is a key tool in mathematics for modeling situations like population decline, radioactive decay, or asset depreciation.<\/p>\n\n\n\n<p>The standard formula for exponential decay is:<br>P(t) = P\u2080(1 &#8211; r)\u1d57<\/p>\n\n\n\n<p>Here is a breakdown of each component of the formula:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>P(t)<\/strong>\u00a0is the final population after a certain amount of time, t. This is what we need to calculate.<\/li>\n\n\n\n<li><strong>P\u2080<\/strong>\u00a0is the initial population at the beginning of the time period. In this problem, the initial population is 2500.<\/li>\n\n\n\n<li><strong>r<\/strong>\u00a0is the rate of decrease per time period, expressed as a decimal. The problem states the population is decreasing at a rate of 3.5% per year. To convert this percentage to a decimal, we divide by 100, which gives us r = 0.035.<\/li>\n\n\n\n<li><strong>t<\/strong>\u00a0is the number of time periods that have passed. In this case, the time period is 5 years.<\/li>\n<\/ul>\n\n\n\n<p>Now, we can substitute the given values into the formula:<br>P(5) = 2500(1 &#8211; 0.035)\u2075<\/p>\n\n\n\n<p>First, we calculate the value inside the parentheses. This term, (1 &#8211; r), is known as the decay factor. It represents the proportion of the population that remains from one year to the next.<br>1 &#8211; 0.035 = 0.965<\/p>\n\n\n\n<p>Our equation now becomes:<br>P(5) = 2500(0.965)\u2075<\/p>\n\n\n\n<p>Next, we calculate (0.965)\u2075, which means multiplying 0.965 by itself five times.<br>(0.965)\u2075 \u2248 0.8368277<\/p>\n\n\n\n<p>Finally, we multiply this result by the initial population:<br>P(5) \u2248 2500 * 0.8368277<br>P(5) \u2248 2092.069<\/p>\n\n\n\n<p>Since population is counted in whole numbers, we round the result to the nearest person. The number 2092.069 rounds down to 2092. Therefore, after 5 years of decreasing at a rate of 3.5% per year, the town&#8217;s population is expected to be 2092.<\/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-banner6-2085.jpeg\" alt=\"\" class=\"wp-image-271683\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The population of the town after 5 years will be approximately&nbsp;2092. Explanation This problem involves exponential decay, which describes how a quantity decreases at a rate proportional to its current value. To solve this, we use the exponential decay formula, which is a key tool in mathematics for modeling [&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-271677","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271677","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=271677"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271677\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271677"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271677"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}