{"id":246145,"date":"2025-07-06T19:54:45","date_gmt":"2025-07-06T19:54:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246145"},"modified":"2025-07-06T19:54:47","modified_gmt":"2025-07-06T19:54:47","slug":"the-population-of-austinberg-on-january-1-2000-was-1-4-million","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/the-population-of-austinberg-on-january-1-2000-was-1-4-million\/","title":{"rendered":"The population of Austinberg on January 1, 2000 was 1.4 million"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">The population of Austinberg on January 1, 2000 was 1.4 million<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-248.png\" alt=\"\" class=\"wp-image-246146\"\/><\/figure>\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>The correct answer is&nbsp;<strong>B) p = 1.4(0.88)\u1d57<\/strong>.<\/p>\n\n\n\n<p>This problem describes a situation of exponential decay, which occurs when a quantity decreases by a consistent percentage over regular time intervals. The general formula for exponential decay is p = P(1 &#8211; r)\u1d57, where &#8216;p&#8217; is the final population, &#8216;P&#8217; is the initial population, &#8216;r&#8217; is the rate of decay expressed as a decimal, and &#8216;t&#8217; is the number of time periods, in this case, years.<\/p>\n\n\n\n<p>First, we must identify the values provided in the problem. The initial population of Austinberg, P, is 1.4 million. The problem states that the population variable &#8216;p&#8217; is already in millions, so we can use the number 1.4 for P in our equation.<\/p>\n\n\n\n<p>Next, we identify the rate of decrease, &#8216;r&#8217;. The population has decreased at a rate of 12% each year. To use this percentage in our formula, we must convert it into a decimal by dividing by 100. So, r = 12% = 12 \/ 100 = 0.12.<\/p>\n\n\n\n<p>The core of the exponential decay formula is the decay factor, which is calculated as (1 &#8211; r). This factor represents the proportion of the population that remains from one year to the next. Since the population decreases by 12%, it means that 100% &#8211; 12% = 88% of the population remains each year. In decimal form, this is calculated as 1 &#8211; 0.12 = 0.88. This value, 0.88, is the base of the exponent in our equation.<\/p>\n\n\n\n<p>Finally, we can assemble the complete equation by substituting the initial population and the decay factor into the formula:<\/p>\n\n\n\n<p>p = P(1 &#8211; r)\u1d57<br>p = 1.4(0.88)\u1d57<\/p>\n\n\n\n<p>This matches option B. The other options are incorrect. Option A incorrectly uses the rate of decay (0.12) as the decay factor. Options C and D model exponential growth because their bases (1.88 and 1.12) are greater than one, indicating an increase in population rather than the stated decrease<\/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-banner5-799.jpeg\" alt=\"\" class=\"wp-image-246147\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The population of Austinberg on January 1, 2000 was 1.4 million The Correct Answer and Explanation is: The correct answer is&nbsp;B) p = 1.4(0.88)\u1d57. This problem describes a situation of exponential decay, which occurs when a quantity decreases by a consistent percentage over regular time intervals. The general formula for exponential decay is p = [&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-246145","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246145","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=246145"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246145\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}