{"id":275928,"date":"2025-07-30T08:29:17","date_gmt":"2025-07-30T08:29:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=275928"},"modified":"2025-07-30T08:29:20","modified_gmt":"2025-07-30T08:29:20","slug":"give-the-rate-of-growth","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/30\/give-the-rate-of-growth\/","title":{"rendered":"Give the rate of growth"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Correct Answer:<\/strong> 7.5%<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

The provided equation, y = 35(1.075)^x, is an example of an exponential growth function. To understand how to find the rate of growth, we can compare it to the standard formula for exponential growth, which is y = a(1 + r)^x.<\/p>\n\n\n\n

In this general formula:<\/p>\n\n\n\n

    \n
  • y\u00a0represents the final amount after a certain number of time periods.<\/li>\n\n\n\n
  • a\u00a0is the initial or starting amount.<\/li>\n\n\n\n
  • r\u00a0is the rate of growth, expressed as a decimal.<\/li>\n\n\n\n
  • x\u00a0represents the number of time periods that have passed.<\/li>\n\n\n\n
  • The term\u00a0(1 + r)\u00a0is known as the growth factor. It represents the original amount (the 1) plus the new growth (the\u00a0r) for each time period.<\/li>\n<\/ul>\n\n\n\n

    Now, let’s match the components of the given equation, y = 35(1.075)^x, to the standard formula:<\/p>\n\n\n\n

      \n
    • The initial amount,\u00a0a, is 35.<\/li>\n\n\n\n
    • The growth factor,\u00a0(1 + r), is 1.075.<\/li>\n<\/ul>\n\n\n\n

      The question asks for the “rate of growth,” which corresponds to the variable r. We can find r by using the growth factor from our equation. We set up the following simple equation:<\/p>\n\n\n\n

      1 + r = 1.075<\/p>\n\n\n\n

      To solve for r, we subtract 1 from both sides of the equation:<\/p>\n\n\n\n

      r = 1.075 – 1
      r = 0.075<\/p>\n\n\n\n

      This gives us the rate of growth as a decimal. To express this rate as a percentage, which is the more common format, we multiply the decimal by 100:<\/p>\n\n\n\n

      0.075 * 100 = 7.5%<\/p>\n\n\n\n

      Therefore, the rate of growth for the function y = 35(1.075)^x is 7.5%. This means that for each unit increase in x, the value of y increases by 7.5% of its previous value.<\/p>\n\n\n\n

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

      The Correct Answer and Explanation is: Correct Answer: 7.5% Explanation The provided equation, y = 35(1.075)^x, is an example of an exponential growth function. To understand how to find the rate of growth, we can compare it to the standard formula for exponential growth, which is y = a(1 + r)^x. In this general formula: Now, let’s match […]<\/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-275928","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275928","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=275928"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/275928\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=275928"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=275928"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=275928"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}