{"id":146347,"date":"2024-09-30T18:58:24","date_gmt":"2024-09-30T18:58:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=146347"},"modified":"2024-09-30T18:58:26","modified_gmt":"2024-09-30T18:58:26","slug":"the-current-value-of-a-new-car-is-24000","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/30\/the-current-value-of-a-new-car-is-24000\/","title":{"rendered":"The current value of a new car is $24,000"},"content":{"rendered":"\n

The current value of a new car is $24,000. The car will depreciate 12% per year over the next 5 years. Which exponential equation models this situation?
A. f(x)=24,000 * 0.12^x
B. f(x)=24,000 * 0.88^x
C. f(x)= 24,000 * 5^x
D. f(x)= 24,000 * 1.12^x<\/p>\n\n\n\n

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

The correct equation is B. f(x) = 24,000 * 0.88^x<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

Depreciation refers to the loss in value of an asset over time. In this case, the car loses 12% of its value each year. To model this depreciation using an exponential function, we start with the general form of an exponential decay equation:<\/p>\n\n\n\n

[
f(x) = P \\cdot (1 – r)^x
]<\/p>\n\n\n\n

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

    \n
  • ( f(x) ) is the value of the car after ( x ) years,<\/li>\n\n\n\n
  • ( P ) is the initial value of the car,<\/li>\n\n\n\n
  • ( r ) is the rate of depreciation (in decimal form), and<\/li>\n\n\n\n
  • ( x ) is the number of years.<\/li>\n<\/ul>\n\n\n\n

    In this case:<\/p>\n\n\n\n

      \n
    • The initial value ( P = 24,000 ),<\/li>\n\n\n\n
    • The depreciation rate ( r = 12\\% ) or 0.12 in decimal form,<\/li>\n\n\n\n
    • The decay factor ( 1 – r = 1 – 0.12 = 0.88 ), which represents retaining 88% of the car’s value each year.<\/li>\n<\/ul>\n\n\n\n

      Thus, the equation that models the car\u2019s depreciation is:<\/p>\n\n\n\n

      [
      f(x) = 24,000 \\cdot 0.88^x
      ]<\/p>\n\n\n\n

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

      Why not the other options?<\/h4>\n\n\n\n
        \n
      • A. f(x) = 24,000 * 0.12^x<\/strong>: This suggests that the car would retain only 12% of its value each year, which is incorrect as the car loses 12%, not keeps only 12%.<\/li>\n\n\n\n
      • C. f(x) = 24,000 * 5^x<\/strong>: This suggests exponential growth rather than decay, which is not applicable in this depreciation scenario.<\/li>\n\n\n\n
      • D. f(x) = 24,000 * 1.12^x<\/strong>: This suggests that the car’s value increases by 12% per year, which is the opposite of what\u2019s happening.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

        The current value of a new car is $24,000. The car will depreciate 12% per year over the next 5 years. Which exponential equation models this situation?A. f(x)=24,000 * 0.12^xB. f(x)=24,000 * 0.88^xC. f(x)= 24,000 * 5^xD. f(x)= 24,000 * 1.12^x The Correct Answer and Explanation is : The correct equation is B. f(x) = […]<\/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-146347","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146347","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=146347"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146347\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}