{"id":216307,"date":"2025-05-19T04:29:25","date_gmt":"2025-05-19T04:29:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=216307"},"modified":"2025-05-19T07:40:58","modified_gmt":"2025-05-19T07:40:58","slug":"each-year-a-group-of-150-alaskan-wolves-has-an-average-birth-rate-of-15-and-an-average-death-rate-of-37-per-year-which-function-could-be-used-to-predict-when-there-will-be-25-wolves-in-this-group","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/19\/each-year-a-group-of-150-alaskan-wolves-has-an-average-birth-rate-of-15-and-an-average-death-rate-of-37-per-year-which-function-could-be-used-to-predict-when-there-will-be-25-wolves-in-this-group\/","title":{"rendered":"Each year, a group of 150 Alaskan wolves has an average birth rate of 15% and an average death rate of 37% per year."},"content":{"rendered":"\n

Each year, a group of 150 Alaskan wolves has an average birth rate of 15% and an average death rate of 37% per year. Which function could be used to predict when there will be 25 wolves in this group? 150(1.15-0.37)^(t)=25, 150((1.15)^(t)-(0.63)^(t))=25, 150(1.15-0.63)^(t)=25, 150((1.15)^(t)-(0.37)^(t))=25<\/p>\n\n\n\n

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

Correct Answer:<\/h3>\n\n\n\n

150(1.15 – 0.37)\u1d57 = 25<\/strong><\/p>\n\n\n\n

\n\n\n\n

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

To determine the number of wolves in the group over time, we need to construct an exponential decay function<\/strong> that models the population change each year based on birth and death rates.<\/p>\n\n\n\n

Step 1: Understand the Given Data<\/h4>\n\n\n\n
    \n
  • Initial wolf population: 150<\/li>\n\n\n\n
  • Annual birth rate: 15% \u2192 This means the population increases by 15% each year<\/strong><\/li>\n\n\n\n
  • Annual death rate: 37% \u2192 This means the population decreases by 37% each year<\/strong><\/li>\n<\/ul>\n\n\n\n

    Since both processes (birth and death) are occurring simultaneously within the same year<\/strong>, we must combine them to determine the net population change per year.<\/p>\n\n\n\n

    Step 2: Calculate the Net Growth Rate<\/h4>\n\n\n\n

    Net growth rate = Birth rate \u2013 Death rate
    Net growth rate = 15% \u2013 37% = \u201322%<\/strong><\/p>\n\n\n\n

    This means the population is decreasing by 22% each year<\/strong>. In decimal form, the growth factor is:<\/p>\n\n\n\n

    1 – 0.22 = 0.78<\/strong><\/p>\n\n\n\n

    So, each year, the population is multiplied by 0.78.<\/p>\n\n\n\n

    Step 3: Create the Exponential Model<\/h4>\n\n\n\n

    An exponential decay function takes the form:<\/p>\n\n\n\n

    P(t) = P\u2080 \u00d7 (r)\u1d57<\/strong><\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • P(t)<\/strong> = population after t years<\/li>\n\n\n\n
    • P\u2080<\/strong> = initial population (150)<\/li>\n\n\n\n
    • r<\/strong> = decay factor (0.78)<\/li>\n\n\n\n
    • t<\/strong> = number of years<\/li>\n<\/ul>\n\n\n\n

      Thus, the function becomes:<\/p>\n\n\n\n

      P(t) = 150 \u00d7 (0.78)\u1d57<\/strong><\/p>\n\n\n\n

      Now, we\u2019re asked to find the equation that models when the population will decrease to 25 wolves, so we set:<\/p>\n\n\n\n

      150 \u00d7 (0.78)\u1d57 = 25<\/strong><\/p>\n\n\n\n

      But note that 0.78 = 1.15 – 0.37<\/strong>, so this can also be written as:<\/p>\n\n\n\n

      150 \u00d7 (1.15 – 0.37)\u1d57 = 25<\/strong><\/p>\n\n\n\n

      This exactly matches the first option:<\/p>\n\n\n\n

      \ud83d\udc49 150(1.15 – 0.37)\u1d57 = 25<\/strong><\/p>\n\n\n\n

      Why the Other Options Are Incorrect:<\/h4>\n\n\n\n
        \n
      • 150((1.15)\u1d57 – (0.63)\u1d57) = 25<\/strong> and others try to subtract exponential terms, which does not<\/strong> reflect a net rate of change and is mathematically incorrect for modeling combined birth-death effects.<\/li>\n\n\n\n
      • Only combining the birth and death rates before exponentiation<\/strong> gives a valid net growth model.<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        Final Answer:<\/h3>\n\n\n\n

        \u2705 150(1.15 – 0.37)\u1d57 = 25<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

        Each year, a group of 150 Alaskan wolves has an average birth rate of 15% and an average death rate of 37% per year. Which function could be used to predict when there will be 25 wolves in this group? 150(1.15-0.37)^(t)=25, 150((1.15)^(t)-(0.63)^(t))=25, 150(1.15-0.63)^(t)=25, 150((1.15)^(t)-(0.37)^(t))=25 The Correct Answer and Explanation is: Correct Answer: 150(1.15 – 0.37)\u1d57 […]<\/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-216307","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216307","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=216307"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216307\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=216307"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=216307"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=216307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}