{"id":188480,"date":"2025-02-07T04:23:36","date_gmt":"2025-02-07T04:23:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188480"},"modified":"2025-02-07T04:23:38","modified_gmt":"2025-02-07T04:23:38","slug":"which-phrase-describes-an-unknown-or-changeable-quantity","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/07\/which-phrase-describes-an-unknown-or-changeable-quantity\/","title":{"rendered":"Which phrase describes an unknown or changeable quantity"},"content":{"rendered":"\n<p>1.\u00a0\u00a0\u00a0 Which phrase describes an unknown or changeable quantity <\/p>\n\n\n\n<p>A. 4 quarts in a gallon <\/p>\n\n\n\n<p>B. 3 feet 7 inchits <\/p>\n\n\n\n<p>C. 2 o&#8217;clock in the afternoon <\/p>\n\n\n\n<p>D. The height of the building times (1)\/(2)<\/p>\n\n\n\n<p>2.&nbsp;&nbsp;&nbsp; the loall gym currently has 100 members. the membership entrollment is increasing at a rate of 8% per year. write an exponential equation for this situation.<\/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<h3 class=\"wp-block-heading\">1. Which phrase describes an unknown or changeable quantity?<\/h3>\n\n\n\n<p>The correct answer is <strong>D. The height of the building times (1)\/(2)<\/strong>.<\/p>\n\n\n\n<p>This option involves a variable that could change depending on the height of the building. The height of the building is an unknown quantity that can vary, and multiplying it by 1\/2 indicates a relationship that can change as the height changes. Therefore, this is the correct choice to describe a changeable quantity.<\/p>\n\n\n\n<p>The other options are specific, fixed quantities:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. 4 quarts in a gallon<\/strong> is a fixed conversion factor.<\/li>\n\n\n\n<li><strong>B. 3 feet 7 inches<\/strong> is a fixed measurement of length.<\/li>\n\n\n\n<li><strong>C. 2 o&#8217;clock in the afternoon<\/strong> is a specific time and does not vary in the context given.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. Exponential Equation for Gym Membership Enrollment<\/h3>\n\n\n\n<p>The gym has 100 members initially, and membership is increasing at a rate of 8% per year. To write an exponential equation that models this situation, we use the general form of an exponential growth equation:<\/p>\n\n\n\n<p>[<br>P(t) = P_0 \\times (1 + r)^t<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(P(t)) is the population (or number of gym members) at time (t),<\/li>\n\n\n\n<li>(P_0) is the initial population (or number of members at the start),<\/li>\n\n\n\n<li>(r) is the growth rate (as a decimal),<\/li>\n\n\n\n<li>(t) is the time in years.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Given values:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial members ((P_0)) = 100<\/li>\n\n\n\n<li>Growth rate ((r)) = 8% = 0.08 (as a decimal)<\/li>\n\n\n\n<li>Time ((t)) is the number of years.<\/li>\n<\/ul>\n\n\n\n<p>So, the exponential equation for this situation becomes:<\/p>\n\n\n\n<p>[<br>P(t) = 100 \\times (1 + 0.08)^t<br>]<\/p>\n\n\n\n<p>[<br>P(t) = 100 \\times (1.08)^t<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Explanation:<\/h4>\n\n\n\n<p>The formula represents exponential growth, where the number of gym members increases by a constant percentage every year. Here\u2019s a breakdown of how it works:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Initial Population (100)<\/strong>: The term (P_0 = 100) reflects that there are 100 members to start with.<\/li>\n\n\n\n<li><strong>Growth Rate (8%)<\/strong>: The growth rate is 8%, which is expressed as a decimal (0.08). Each year, the gym\u2019s membership increases by 8% of the current membership.<\/li>\n\n\n\n<li><strong>Time ((t))<\/strong>: The variable (t) represents the number of years that have passed. As time increases, the number of gym members will increase exponentially because of the compounding growth rate.<\/li>\n<\/ol>\n\n\n\n<p>At the end of the first year, for example, the number of members would be:<\/p>\n\n\n\n<p>[<br>P(1) = 100 \\times 1.08 = 108 \\text{ members}<br>]<\/p>\n\n\n\n<p>At the end of the second year, the number would increase again by 8%, so:<\/p>\n\n\n\n<p>[<br>P(2) = 100 \\times 1.08^2 \\approx 116.64 \\text{ members}<br>]<\/p>\n\n\n\n<p>This equation is useful for predicting future membership growth based on the given rate of increase.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1.\u00a0\u00a0\u00a0 Which phrase describes an unknown or changeable quantity A. 4 quarts in a gallon B. 3 feet 7 inchits C. 2 o&#8217;clock in the afternoon D. The height of the building times (1)\/(2) 2.&nbsp;&nbsp;&nbsp; the loall gym currently has 100 members. the membership entrollment is increasing at a rate of 8% per year. write [&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-188480","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188480","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=188480"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188480\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188480"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188480"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188480"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}