{"id":275005,"date":"2025-07-28T13:46:56","date_gmt":"2025-07-28T13:46:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=275005"},"modified":"2025-07-28T13:47:01","modified_gmt":"2025-07-28T13:47:01","slug":"the-function-ft-12000-1-075-t-models-the-value-of-an-investment-t-years-from-now","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/28\/the-function-ft-12000-1-075-t-models-the-value-of-an-investment-t-years-from-now\/","title":{"rendered":"The function f(t) = 12000 * (1.075) ^ t models the value of an investment t years from now"},"content":{"rendered":"\n<p>The function f(t) = 12000 * (1.075) ^ t models the value of an investment t years from now. What is the meaning of the value of \/(5)?<br>OA. the interest rate the investment earns<br>B. the value of the investment 5 years ago<br>C. the initial value of the investment<br>D. the value of the investment in 5 years<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>D. the value of the investment in 5 years<\/strong>.<\/p>\n\n\n\n<p>The function f(t)=12000\u00d7(1.075)tf(t) = 12000 \\times (1.075)^t models the value of an investment at time tt years from the present. Here\u2019s the breakdown of each part of the formula:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>12000<\/strong>: This represents the initial value of the investment at time t=0t = 0. It is the principal amount that was originally invested.<\/li>\n\n\n\n<li><strong>(1.075)^t<\/strong>: This is the factor by which the investment grows each year. The base of 1.0751.075 indicates that the investment grows by 7.5% per year (since 1+0.075=1.0751 + 0.075 = 1.075).<\/li>\n\n\n\n<li><strong>t<\/strong>: This is the number of years into the future for which the value is being calculated. As tt increases, the investment grows.<\/li>\n<\/ol>\n\n\n\n<p>When we want to know f(5)f(5), it means we are calculating the value of the investment after 5 years. To find this, substitute t=5t = 5 into the equation: f(5)=12000\u00d7(1.075)5f(5) = 12000 \\times (1.075)^5<\/p>\n\n\n\n<p>Using a calculator, we find: f(5)\u224812000\u00d71.441f(5) \\approx 12000 \\times 1.441 f(5)\u224817292f(5) \\approx 17292<\/p>\n\n\n\n<p>This shows that the value of the investment after 5 years is approximately $17,292.<\/p>\n\n\n\n<p>Thus, <strong>f(5)f(5)<\/strong> gives the <strong>value of the investment in 5 years<\/strong> based on the growth formula. Therefore, option <strong>D<\/strong> is the correct interpretation of the function value at t=5t = 5.<\/p>\n\n\n\n<p>Let\u2019s rule out the other options:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A<\/strong> (the interest rate) is incorrect because the interest rate is part of the formula but not the direct result of evaluating f(5)f(5).<\/li>\n\n\n\n<li><strong>B<\/strong> (the value of the investment 5 years ago) is incorrect because f(t)f(t) gives future values, not past values.<\/li>\n\n\n\n<li><strong>C<\/strong> (the initial value of the investment) is incorrect because the initial value, 1200012000, is not calculated by the function f(t)f(t); it is simply a part of the formula.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the correct interpretation of f(5)f(5) is the <strong>value of the investment in 5 years<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The function f(t) = 12000 * (1.075) ^ t models the value of an investment t years from now. What is the meaning of the value of \/(5)?OA. the interest rate the investment earnsB. the value of the investment 5 years agoC. the initial value of the investmentD. the value of the investment in 5 [&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-275005","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275005","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=275005"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275005\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=275005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=275005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=275005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}