{"id":222201,"date":"2025-05-31T06:35:20","date_gmt":"2025-05-31T06:35:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222201"},"modified":"2025-05-31T06:35:22","modified_gmt":"2025-05-31T06:35:22","slug":"annual-revenue-for-corning-supplies-grew-by-5-5-in-2007-1-1-in-2008-3-5-in-2009-1-1-in-2010-and-1-8-in-2011","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/31\/annual-revenue-for-corning-supplies-grew-by-5-5-in-2007-1-1-in-2008-3-5-in-2009-1-1-in-2010-and-1-8-in-2011\/","title":{"rendered":"Annual revenue for Corning Supplies grew by 5.5% in 2007; 1.1% in 2008; -3.5% in 2009; -1.1% in 2010; and 1.8% in 2011."},"content":{"rendered":"\n

Annual revenue for Corning Supplies grew by 5.5% in 2007; 1.1% in 2008; -3.5% in 2009; -1.1% in 2010; and 1.8% in 2011.<\/p>\n\n\n\n

What is the mean growth annual rate over this period? Round your answer to four decimal places. Do not round intermediate calculations.<\/p>\n\n\n\n

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

To calculate the mean annual growth rate<\/strong> over the period 2007 to 2011, we use the geometric mean<\/strong> formula for growth rates rather than the arithmetic mean. The geometric mean accounts for compounding over time, which is essential in understanding average growth rates for financial data.<\/p>\n\n\n\n

\n\n\n\n

Step-by-step Calculation<\/strong><\/h3>\n\n\n\n

The given annual growth rates are:<\/p>\n\n\n\n

    \n
  • 2007: +5.5% \u2192 1 + 0.055 = 1.055<\/strong><\/li>\n\n\n\n
  • 2008: +1.1% \u2192 1 + 0.011 = 1.011<\/strong><\/li>\n\n\n\n
  • 2009: \u22123.5% \u2192 1 \u2212 0.035 = 0.965<\/strong><\/li>\n\n\n\n
  • 2010: \u22121.1% \u2192 1 \u2212 0.011 = 0.989<\/strong><\/li>\n\n\n\n
  • 2011: +1.8% \u2192 1 + 0.018 = 1.018<\/strong><\/li>\n<\/ul>\n\n\n\n

    Now compute the geometric mean<\/strong>: Geometric Mean=(1.055\u00d71.011\u00d70.965\u00d70.989\u00d71.018)1\/5\\text{Geometric Mean} = \\left(1.055 \\times 1.011 \\times 0.965 \\times 0.989 \\times 1.018\\right)^{1\/5} =(1.038345646)1\/5\u22481.007545= (1.038345646)^{1\/5} \\approx 1.007545<\/p>\n\n\n\n

    Convert this back to a percentage growth rate: 1.007545\u22121=0.007545\u21d20.7545%1.007545 – 1 = 0.007545 \\Rightarrow \\boxed{0.7545\\%}<\/p>\n\n\n\n

    \n\n\n\n

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

    When evaluating average growth over multiple years, it\u2019s essential to consider how the changes compound over time. The arithmetic mean, which simply averages the percentages, does not account for this compounding effect. Instead, we use the geometric mean<\/strong> to calculate the mean annual growth rate (MAGR)<\/strong> because it reflects the cumulative impact of year-over-year growth.<\/p>\n\n\n\n

    In this case, Corning Supplies had growth rates that varied widely\u2014some years with positive growth and others with declines. The compounding impact of these fluctuations must be considered to assess the company\u2019s true average performance over the 5-year period.<\/p>\n\n\n\n

    The process begins by converting each percentage change into a growth factor (e.g., 5.5% becomes 1.055). Multiplying all five growth factors together gives the total cumulative growth over the period. Taking the fifth root (since there are five years) of the product yields the geometric mean growth factor. Subtracting 1 and converting to a percentage gives the mean annual growth rate<\/strong>.<\/p>\n\n\n\n

    Using this method, we find Corning Supplies experienced an average annual growth rate of approximately 0.7545%<\/strong> from 2007 to 2011. This result suggests that despite the ups and downs\u2014including two years of negative growth\u2014the company still maintained slight positive average growth over the entire period.<\/p>\n\n\n\n

    This metric provides a more accurate and meaningful measure of performance over time, especially when comparing with other firms or evaluating long-term trends.<\/p>\n\n\n\n

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

    Annual revenue for Corning Supplies grew by 5.5% in 2007; 1.1% in 2008; -3.5% in 2009; -1.1% in 2010; and 1.8% in 2011. What is the mean growth annual rate over this period? Round your answer to four decimal places. Do not round intermediate calculations. The Correct Answer and Explanation is: To calculate the mean […]<\/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-222201","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222201","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=222201"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222201\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222201"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222201"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222201"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}