{"id":148016,"date":"2024-10-04T05:38:52","date_gmt":"2024-10-04T05:38:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=148016"},"modified":"2024-10-04T05:38:55","modified_gmt":"2024-10-04T05:38:55","slug":"which-expression-could-complete-the-equation-used-to-solve-the-problem","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/04\/which-expression-could-complete-the-equation-used-to-solve-the-problem\/","title":{"rendered":"Which expression could complete the equation used to solve the problem"},"content":{"rendered":"\n<p>Which expression could complete the equation used to solve the problem?<br>Today, a motorcycle is valued at $35.000. The value is expected to decrease at a rate of 7.5% each year. What is the value of the motorcycle expected to be 5 years from now?<br>y=35,000.=<em>_<\/em><br>a. (7.5)\u2075<br>b. (1.075)\u2075<br>c. (0.925)\u2075<br>d. (92.5)\u2075<br>e. (0.075)\u2075<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the value of the motorcycle five years from now, given that its current value is $35,000 and it depreciates at a rate of 7.5% per year, we need to utilize the formula for exponential decay. The value of an asset after a certain period of depreciation can be calculated using the formula:<\/p>\n\n\n\n<p>[<br>V = P(1 &#8211; r)^t<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( V ) is the future value of the asset,<\/li>\n\n\n\n<li>( P ) is the present value (initial value),<\/li>\n\n\n\n<li>( r ) is the rate of depreciation (expressed as a decimal), and<\/li>\n\n\n\n<li>( t ) is the number of years.<\/li>\n<\/ul>\n\n\n\n<p>In this problem:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The present value ( P = 35,000 )<\/li>\n\n\n\n<li>The depreciation rate ( r = 0.075 ) (which is 7.5% expressed as a decimal)<\/li>\n\n\n\n<li>The time ( t = 5 ) years<\/li>\n<\/ul>\n\n\n\n<p>The first step is to compute ( 1 &#8211; r ):<\/p>\n\n\n\n<p>[<br>1 &#8211; r = 1 &#8211; 0.075 = 0.925<br>]<\/p>\n\n\n\n<p>Now, we substitute these values into the formula:<\/p>\n\n\n\n<p>[<br>V = 35,000 \\times (0.925)^5<br>]<\/p>\n\n\n\n<p>This shows that the expression ( (0.925)^5 ) is crucial in calculating the motorcycle&#8217;s value in 5 years. The expression describes the remaining value of the motorcycle after 5 years of depreciation at 7.5% per year.<\/p>\n\n\n\n<p>Now, let&#8217;s analyze the options given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>a. (7.5)\u2075<\/strong>: This does not represent depreciation; it&#8217;s simply raising the percentage to the fifth power.<\/li>\n\n\n\n<li><strong>b. (1.075)\u2075<\/strong>: This represents appreciation (not depreciation) and is incorrect in this context.<\/li>\n\n\n\n<li><strong>c. (0.925)\u2075<\/strong>: This correctly represents the depreciation over 5 years.<\/li>\n\n\n\n<li><strong>d. (92.5)\u2075<\/strong>: This is incorrect as it does not relate to depreciation at all.<\/li>\n\n\n\n<li><strong>e. (0.075)\u2075<\/strong>: This is also incorrect; it doesn\u2019t relate to the depreciation calculation.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the correct answer is <strong>c. (0.925)\u2075<\/strong>.<\/p>\n\n\n\n<p>In summary, to find the value of the motorcycle after 5 years, we would multiply the initial value of $35,000 by ( (0.925)^5 ), reflecting the impact of annual depreciation on its overall value.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which expression could complete the equation used to solve the problem?Today, a motorcycle is valued at $35.000. The value is expected to decrease at a rate of 7.5% each year. What is the value of the motorcycle expected to be 5 years from now?y=35,000.=_a. (7.5)\u2075b. (1.075)\u2075c. (0.925)\u2075d. (92.5)\u2075e. (0.075)\u2075 The Correct Answer and Explanation is [&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-148016","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148016","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=148016"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148016\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=148016"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=148016"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=148016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}