{"id":271482,"date":"2025-07-26T03:21:58","date_gmt":"2025-07-26T03:21:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271482"},"modified":"2025-07-26T03:22:06","modified_gmt":"2025-07-26T03:22:06","slug":"you-decide-to-buy-a-brand-new-car-that-costs-42000","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/26\/you-decide-to-buy-a-brand-new-car-that-costs-42000\/","title":{"rendered":"You decide to buy a brand new car that costs $42,000.\u00a0"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-705.png\" alt=\"\" class=\"wp-image-271483\"\/><\/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>f(x) = 42000(0.925)\u02e3<\/strong>.<\/p>\n\n\n\n<p>This problem involves modeling exponential decay, which describes a quantity decreasing at a rate proportional to its current value. The general formula for exponential growth or decay is f(x) = A(b)\u02e3, where A is the initial amount, b is the growth or decay factor, and x is the number of time periods.<\/p>\n\n\n\n<p>In this specific scenario, we are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The initial value of the car, which is our starting amount, A. Here, A = $42,000.<\/li>\n\n\n\n<li>The rate of depreciation, which is 7.5% per year. Depreciation means the value is decreasing, so we are dealing with exponential decay.<\/li>\n<\/ul>\n\n\n\n<p>To find the correct formula, we need to determine the decay factor, &#8216;b&#8217;. The decay factor is calculated as (1 &#8211; r), where &#8216;r&#8217; is the rate of decay expressed as a decimal.<\/p>\n\n\n\n<p>First, we must convert the percentage rate into a decimal:<br>r = 7.5% = 7.5 \/ 100 = 0.075<\/p>\n\n\n\n<p>Next, we calculate the decay factor &#8216;b&#8217;:<br>b = 1 &#8211; r = 1 &#8211; 0.075 = 0.925<br>This decay factor of 0.925 signifies that the car retains 92.5% of its value each year, which is equivalent to losing 7.5% of its value.<\/p>\n\n\n\n<p>Now, we can substitute the initial value (A = 42000) and the decay factor (b = 0.925) into the general exponential formula:<br>f(x) = A(b)\u02e3<br>f(x) = 42000(0.925)\u02e3<\/p>\n\n\n\n<p>Let&#8217;s examine why the other options are incorrect:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>f(x) = 42000(1.075)\u02e3: This formula models exponential growth, not decay, because the base (1.075) is greater than 1. This would represent the car&#8217;s value increasing by 7.5% each year.<\/li>\n\n\n\n<li>f(x) = 42000(.075)\u02e3: This formula incorrectly uses the decimal rate (0.075) as the decay factor. This would imply a depreciation of 92.5% each year (1 &#8211; 0.075), which is a much faster loss of value than stated.<\/li>\n\n\n\n<li>f(x) = 75(1.42)\u02e3: This formula uses an incorrect initial value ($75) and models exponential growth at a rate of 42%.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the only formula that correctly models the car&#8217;s worth starting at $42,000 and depreciating by 7.5% annually is f(x) = 42000(0.925)\u02e3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2048.jpeg\" alt=\"\" class=\"wp-image-271484\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;f(x) = 42000(0.925)\u02e3. This problem involves modeling exponential decay, which describes a quantity decreasing at a rate proportional to its current value. The general formula for exponential growth or decay is f(x) = A(b)\u02e3, where A is the initial amount, b is the growth or decay [&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-271482","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271482","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=271482"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271482\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}