{"id":278854,"date":"2025-08-02T12:16:24","date_gmt":"2025-08-02T12:16:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=278854"},"modified":"2025-08-02T12:16:26","modified_gmt":"2025-08-02T12:16:26","slug":"john-just-purchased-a-new-car-with-a-value-of-35000","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/02\/john-just-purchased-a-new-car-with-a-value-of-35000\/","title":{"rendered":"John just purchased a new car with a value of $35,000.\u00a0"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-182.png\" alt=\"\" class=\"wp-image-278855\"\/><\/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>a. y = 35000(0.925)^x<\/strong><\/p>\n\n\n\n<p>This problem describes a situation of exponential decay, where an initial value decreases by a fixed percentage over regular time intervals. The general formula for exponential growth or decay is y = a(1 \u00b1 r)^x.<\/p>\n\n\n\n<p>Let&#8217;s break down the components of this formula in the context of the question:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>y<\/strong>\u00a0represents the final value of the car after a certain amount of time.<\/li>\n\n\n\n<li><strong>a<\/strong>\u00a0is the initial value or starting amount. In this case, the car was purchased for $35,000, so a = 35,000.<\/li>\n\n\n\n<li><strong>r<\/strong>\u00a0is the rate of change per time period, expressed as a decimal. The problem states the car &#8220;loses value,&#8221; which indicates decay or a decrease. The rate is 7.5%. To use this in the formula, we must convert the percentage to a decimal by dividing by 100: r = 7.5 \/ 100 = 0.075.<\/li>\n\n\n\n<li><strong>x<\/strong>\u00a0represents the number of time periods that have passed. Here, x is the number of years John has owned the car.<\/li>\n<\/ul>\n\n\n\n<p>Since the car&#8217;s value is decreasing, we use the subtraction form of the general formula: y = a(1 &#8211; r)^x.<\/p>\n\n\n\n<p>Now, we can substitute the known values into this formula:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Start with the decay formula: y = a(1 &#8211; r)^x<\/li>\n\n\n\n<li>Substitute the initial value for &#8216;a&#8217;: y = 35000(1 &#8211; r)^x<\/li>\n\n\n\n<li>Substitute the decay rate for &#8216;r&#8217;: y = 35000(1 &#8211; 0.075)^x<\/li>\n\n\n\n<li>Calculate the value inside the parentheses, which is known as the decay factor: 1 &#8211; 0.075 = 0.925. This factor means that each year, the car retains 92.5% of its value from the previous year.<\/li>\n\n\n\n<li>The final equation is: y = 35000(0.925)^x.<\/li>\n<\/ol>\n\n\n\n<p>This equation accurately models the car&#8217;s value, y, starting at $35,000 and decreasing by 7.5% each year for x years. Comparing our result to the given options, it perfectly matches option a. Option c, with a factor of (1.075), would incorrectly represent an annual increase in value, or appreciation. Other options either misuse the initial value and rate or use an incorrect decay factor.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner5-86.jpeg\" alt=\"\" class=\"wp-image-278856\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;a. y = 35000(0.925)^x This problem describes a situation of exponential decay, where an initial value decreases by a fixed percentage over regular time intervals. The general formula for exponential growth or decay is y = a(1 \u00b1 r)^x. Let&#8217;s break down the components of this [&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-278854","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278854","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=278854"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278854\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=278854"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=278854"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=278854"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}