{"id":276435,"date":"2025-07-31T05:46:39","date_gmt":"2025-07-31T05:46:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=276435"},"modified":"2025-07-31T05:46:41","modified_gmt":"2025-07-31T05:46:41","slug":"a-home-has-an-original-value-of-249000","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/31\/a-home-has-an-original-value-of-249000\/","title":{"rendered":"A home has an original value of $249,000."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

The correct answer is V(t) = 249,000(0.929)^t<\/strong>.<\/p>\n\n\n\n

This problem describes a situation of exponential decay, where an initial value decreases by a fixed percentage over regular time intervals. The general formula for exponential change is V(t) = P(1 + r)^t, where V(t) is the final value after time t, P is the initial principal amount, and r is the annual rate of change.<\/p>\n\n\n\n

In this scenario, the initial value of the home, represented by P, is $249,000. The problem states that the value of the home decreases by 7.1% each year. This percentage is the rate of decay.<\/p>\n\n\n\n

To use this rate in the formula, we must first convert it from a percentage to a decimal. We do this by dividing the percentage by 100:
7.1% = 7.1 \/ 100 = 0.071<\/p>\n\n\n\n

Since the value is decreasing, the rate ‘r’ is negative, so r = -0.071.<\/p>\n\n\n\n

Next, we calculate the expression inside the parentheses, (1 + r), which is known as the decay factor. This factor represents the percentage of the value that remains each year.
Decay Factor = 1 + r = 1 + (-0.071) = 1 – 0.071 = 0.929<\/p>\n\n\n\n

This decay factor of 0.929 means that each year, the home’s value is 92.9% of its value from the previous year. This is equivalent to losing 7.1% of its value annually (100% – 92.9% = 7.1%).<\/p>\n\n\n\n

Finally, we substitute the initial value (P = 249,000) and the decay factor (0.929) into the general exponential formula to model the situation after t years:
V(t) = 249,000(0.929)^t<\/p>\n\n\n\n

This equation accurately represents the value of the home, V(t), after t years of depreciation.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: The correct answer is V(t) = 249,000(0.929)^t. This problem describes a situation of exponential decay, where an initial value decreases by a fixed percentage over regular time intervals. The general formula for exponential change is V(t) = P(1 + r)^t, where V(t) is the final value after time t, P […]<\/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-276435","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/276435","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=276435"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/276435\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=276435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=276435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=276435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}