{"id":230443,"date":"2025-06-09T14:42:42","date_gmt":"2025-06-09T14:42:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230443"},"modified":"2025-06-09T14:42:44","modified_gmt":"2025-06-09T14:42:44","slug":"jason-estimates-that-his-car-loses-12-of-its-value-every-year-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/jason-estimates-that-his-car-loses-12-of-its-value-every-year-2\/","title":{"rendered":"Jason estimates that his car loses 12% of its value every year"},"content":{"rendered":"\n

Jason estimates that his car loses 12% of its value every year. The initial value is $12,000. Which best describes the<\/p>\n\n\n\n

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

Correct Answer:<\/strong><\/h3>\n\n\n\n

The car\u2019s value after ttt years can be modeled by the equation:V(t)=12000\u00d7(0.88)tV(t) = 12000 \\times (0.88)^tV(t)=12000\u00d7(0.88)t<\/p>\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

When an object loses a fixed percentage of its value each year, this is called exponential decay<\/strong>. The general formula for exponential decay is:V(t)=V0\u00d7(1\u2212r)tV(t) = V_0 \\times (1 – r)^tV(t)=V0\u200b\u00d7(1\u2212r)t<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n

    \n
  • V(t)V(t)V(t) is the value after ttt years,<\/li>\n\n\n\n
  • V0V_0V0\u200b is the initial value,<\/li>\n\n\n\n
  • rrr is the decay rate (as a decimal),<\/li>\n\n\n\n
  • ttt is the number of years.<\/li>\n<\/ul>\n\n\n\n

    In Jason\u2019s case:<\/p>\n\n\n\n

      \n
    • The initial value of the car V0=12,000V_0 = 12,000V0\u200b=12,000 dollars,<\/li>\n\n\n\n
    • The annual rate of depreciation r=12%=0.12r = 12\\% = 0.12r=12%=0.12.<\/li>\n<\/ul>\n\n\n\n

      So the formula becomes:V(t)=12000\u00d7(1\u22120.12)t=12000\u00d7(0.88)tV(t) = 12000 \\times (1 – 0.12)^t = 12000 \\times (0.88)^tV(t)=12000\u00d7(1\u22120.12)t=12000\u00d7(0.88)t<\/p>\n\n\n\n

      This means that each year, the car retains 88% of its value from the previous year. For example:<\/p>\n\n\n\n

        \n
      • After 1 year:
        V(1)=12000\u00d70.88=10560V(1) = 12000 \\times 0.88 = 10560V(1)=12000\u00d70.88=10560<\/li>\n\n\n\n
      • After 2 years:
        V(2)=12000\u00d7(0.88)2=9292.8V(2) = 12000 \\times (0.88)^2 = 9292.8V(2)=12000\u00d7(0.88)2=9292.8<\/li>\n\n\n\n
      • After 3 years:
        V(3)=12000\u00d7(0.88)3\u22488177.66V(3) = 12000 \\times (0.88)^3 \\approx 8177.66V(3)=12000\u00d7(0.88)3\u22488177.66<\/li>\n<\/ul>\n\n\n\n

        This model accurately shows that the car’s value declines more slowly over time \u2014 a hallmark of exponential decay. The biggest drop happens early, and the decline gets smaller each year.<\/p>\n\n\n\n

        In summary, the best way to describe the car\u2019s depreciating value is with the equation:V(t)=12000\u00d7(0.88)tV(t) = 12000 \\times (0.88)^tV(t)=12000\u00d7(0.88)t<\/p>\n\n\n\n

        This exponential equation provides a reliable estimate of the car\u2019s value for any year ttt, accounting for a consistent 12% annual decrea<\/p>\n\n\n\n

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

        Jason estimates that his car loses 12% of its value every year. The initial value is $12,000. Which best describes the The Correct Answer and Explanation is: Correct Answer: The car\u2019s value after ttt years can be modeled by the equation:V(t)=12000\u00d7(0.88)tV(t) = 12000 \\times (0.88)^tV(t)=12000\u00d7(0.88)t Explanation When an object loses a fixed percentage of its […]<\/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-230443","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230443","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=230443"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230443\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230443"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230443"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230443"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}