{"id":278867,"date":"2025-08-02T12:36:33","date_gmt":"2025-08-02T12:36:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=278867"},"modified":"2025-08-02T12:36:35","modified_gmt":"2025-08-02T12:36:35","slug":"john-just-purchased-a-new-car-with-a-value-of-35000-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/02\/john-just-purchased-a-new-car-with-a-value-of-35000-2\/","title":{"rendered":"John just purchased a new car with a value of $35,000"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is y = 35000(0.925)^x<\/strong>.<\/p>\n\n\n\n

This problem requires creating an equation to model exponential decay, which describes a quantity decreasing at a constant percentage rate over time. The standard mathematical formula for exponential decay is y = A(1 – r)^x. Understanding each part of this formula is key to finding the correct solution.<\/p>\n\n\n\n

In this formula, ‘y’ represents the final value after a certain period. ‘A’ stands for the initial amount or the starting value. ‘r’ is the rate of decay, which must be expressed as a decimal. Lastly, ‘x’ represents the number of time intervals that have passed, which in this case is the number of years.<\/p>\n\n\n\n

According to the problem, the initial value of the new car, ‘A’, is $35,000. The car loses value, or depreciates, at a rate of 7.5% per year. To use this percentage in our formula, we need to convert it into a decimal by dividing it by 100. This calculation gives us r = 7.5 \/ 100 = 0.075.<\/p>\n\n\n\n

The core of the exponential decay formula is the decay factor, calculated as (1 – r). This factor represents the proportion of the value that remains after each time period. For this car, the decay factor is 1 – 0.075 = 0.925. This means that each year, the car retains 92.5% of its value from the previous year.<\/p>\n\n\n\n

By substituting the initial value (A = 35000) and the calculated decay factor (0.925) into the standard formula, we arrive at the correct equation: y = 35000(0.925)^x. This equation accurately models the value of the car, ‘y’, after ‘x’ years. Other options are incorrect because they either represent growth (using a factor greater than 1) or have an incorrect structure.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

The Correct Answer and Explanation is: The correct answer is y = 35000(0.925)^x. This problem requires creating an equation to model exponential decay, which describes a quantity decreasing at a constant percentage rate over time. The standard mathematical formula for exponential decay is y = A(1 – r)^x. Understanding each part of this formula is key […]<\/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-278867","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278867","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=278867"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278867\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=278867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=278867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=278867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}