{"id":167227,"date":"2024-11-15T08:28:13","date_gmt":"2024-11-15T08:28:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167227"},"modified":"2024-11-15T08:28:15","modified_gmt":"2024-11-15T08:28:15","slug":"a-new-fitness-center-opened-up-with-24-clients","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/a-new-fitness-center-opened-up-with-24-clients\/","title":{"rendered":"A new fitness center opened up with 24 clients."},"content":{"rendered":"\n<p>A new fitness center opened up with 24 clients. Each week they are signing up an average of 5 new members. The business owner wrote the explicit formula for this situation as being A(n) = 24 + (n &#8211; 1)(5). Is this correct for this situation? Justify your answer using complete sentences and proper grammar.<\/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 explicit formula provided by the business owner, ( A(n) = 24 + (n &#8211; 1)(5) ), is correct, but let&#8217;s break it down to fully understand why and provide a clearer formula for this situation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Understanding the Situation<\/h3>\n\n\n\n<p>The fitness center initially has 24 clients. Each week, 5 new members are signing up. This means that the total number of clients is increasing by 5 each week, starting from 24 clients.<\/p>\n\n\n\n<p>In mathematical terms:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The initial number of clients is 24.<\/li>\n\n\n\n<li>The change in the number of clients each week is 5.<\/li>\n\n\n\n<li>We are interested in finding out how many clients there are after (n) weeks.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Understanding the Formula<\/h3>\n\n\n\n<p>The business owner used the formula ( A(n) = 24 + (n &#8211; 1)(5) ).<\/p>\n\n\n\n<p>Here\u2019s how we can interpret the formula:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>24<\/strong> is the initial number of clients when (n = 1) (the first week).<\/li>\n\n\n\n<li><strong>(n &#8211; 1)<\/strong> represents the number of weeks that have passed since the first week, since the first term, 24, corresponds to (n = 1).<\/li>\n\n\n\n<li><strong>5<\/strong> is the number of new clients signing up each week. Therefore, multiplying (n &#8211; 1) by 5 gives the total increase in clients after (n &#8211; 1) weeks.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Verifying the Formula<\/h3>\n\n\n\n<p>Let&#8217;s verify the formula with a couple of values for (n):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For (n = 1):<br>[ A(1) = 24 + (1 &#8211; 1)(5) = 24 + 0 = 24. ]<br>This matches the initial number of clients.<\/li>\n\n\n\n<li>For (n = 2):<br>[ A(2) = 24 + (2 &#8211; 1)(5) = 24 + 5 = 29. ]<br>This is correct, as 5 new clients joined, bringing the total to 29.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the formula correctly calculates the total number of clients for any given week.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: A Clearer Formula<\/h3>\n\n\n\n<p>A more standard explicit formula for this type of situation would be:<br>[ A(n) = 24 + 5(n &#8211; 1). ]<br>This formula is essentially the same but is often written more clearly. If we distribute the 5 across (n &#8211; 1), we get:<br>[ A(n) = 24 + 5n &#8211; 5, ]<br>which simplifies to:<br>[ A(n) = 19 + 5n. ]<\/p>\n\n\n\n<p>Both forms are equivalent, but the more direct formula ( A(n) = 19 + 5n ) can be easier to work with for general cases. Therefore, while the business owner\u2019s formula is correct, a clearer version would be ( A(n) = 19 + 5n ).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A new fitness center opened up with 24 clients. Each week they are signing up an average of 5 new members. The business owner wrote the explicit formula for this situation as being A(n) = 24 + (n &#8211; 1)(5). Is this correct for this situation? Justify your answer using complete sentences and proper grammar. [&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-167227","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167227","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=167227"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167227\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167227"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167227"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167227"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}