{"id":166636,"date":"2024-11-13T23:18:54","date_gmt":"2024-11-13T23:18:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=166636"},"modified":"2024-11-13T23:18:56","modified_gmt":"2024-11-13T23:18:56","slug":"jason-estimates-that-his-car-loses-12-of-its-value-every-year","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/13\/jason-estimates-that-his-car-loses-12-of-its-value-every-year\/","title":{"rendered":"Jason estimates that his car loses 12% of its value every year."},"content":{"rendered":"\n<p>Jason estimates that his car loses 12% of its value every year. The initial value is $12,000. Which best describes the graph of the function that represents the value of the car after x years?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The graph of the function that represents the value of Jason&#8217;s car after <strong>x years<\/strong> is <strong>exponential decay<\/strong>.<\/p>\n\n\n\n<p>To explain why, let&#8217;s break down the problem:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. <strong>Understanding the problem:<\/strong><\/h3>\n\n\n\n<p>Jason estimates that his car loses 12% of its value each year. This means that every year, the car retains 88% (or 1 &#8211; 0.12) of its value. The initial value of the car is $12,000.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. <strong>Mathematical representation:<\/strong><\/h3>\n\n\n\n<p>We can represent the value of the car as a function of time using the formula for exponential decay:<\/p>\n\n\n\n<p>[<br>V(x) = P \\times (1 &#8211; r)^x<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(V(x)) is the value of the car after (x) years.<\/li>\n\n\n\n<li>(P) is the initial value of the car (in this case, $12,000).<\/li>\n\n\n\n<li>(r) is the rate of decay (12%, or 0.12).<\/li>\n\n\n\n<li>(x) is the number of years.<\/li>\n<\/ul>\n\n\n\n<p>Substituting the known values into the formula:<\/p>\n\n\n\n<p>[<br>V(x) = 12,000 \\times (1 &#8211; 0.12)^x<br>]<br>[<br>V(x) = 12,000 \\times 0.88^x<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. <strong>Exponential decay:<\/strong><\/h3>\n\n\n\n<p>In this equation, (0.88^x) represents the exponential decay factor. The factor (0.88) is less than 1, which is characteristic of decay (rather than growth). As (x) (the number of years) increases, the value of (V(x)) decreases, showing the depreciation of the car over time.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. <strong>Graphical interpretation:<\/strong><\/h3>\n\n\n\n<p>The graph of this function would be a <strong>decaying exponential curve<\/strong>. At (x = 0), the value of the car is at its maximum, $12,000. As (x) increases, the value of the car decreases steadily and approaches zero but never quite reaches it. This creates a downward-sloping curve that flattens out as it moves to the right, showing the continuous depreciation of the car.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5. <strong>Conclusion:<\/strong><\/h3>\n\n\n\n<p>The correct description of the graph is <strong>exponential decay<\/strong> because the value of the car decreases by a fixed percentage (12%) each year, which is the defining characteristic of exponential decay.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jason estimates that his car loses 12% of its value every year. The initial value is $12,000. Which best describes the graph of the function that represents the value of the car after x years? The Correct Answer and Explanation is: The graph of the function that represents the value of Jason&#8217;s car after x [&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-166636","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166636","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=166636"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166636\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=166636"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=166636"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=166636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}