{"id":232883,"date":"2025-06-12T10:04:05","date_gmt":"2025-06-12T10:04:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232883"},"modified":"2025-06-12T10:04:07","modified_gmt":"2025-06-12T10:04:07","slug":"the-table-shows-two-sloth-populations-growing-over-time","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/the-table-shows-two-sloth-populations-growing-over-time\/","title":{"rendered":"The table shows two sloth populations growing over time."},"content":{"rendered":"\n

The table shows two sloth populations growing over time. time population 1 population 2 (years since 1990) (thousands) (thousands) 0 90.0 39 1 76.5 37 2 65.0 35 3 55.3 33 4 47.0 31 5 6 7 8 a. Describe a pattern in how each population changed from one year to the next. b. These patterns continued for many years. Based on this information, fill in the extra rows in the table. c. On the same axes, draw graphs of the two populations over time. d. Does Population 2 ever equal Population 1? If so, when? Explain or show your reasoning.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

a. Describe a pattern in how each population changed from one year to the next.<\/strong><\/h3>\n\n\n\n
    \n
  • Population 1:<\/strong>\u00a0This population shows a pattern of\u00a0exponential decay<\/strong>. Each year, the population is approximately 85% of the population from the previous year. We can see this by dividing a year’s population by the previous year’s population (e.g., 76.5 \u00f7 90.0 = 0.85; 65.0 \u00f7 76.5 \u2248 0.85). This means the population is decreasing by 15% each year.<\/li>\n\n\n\n
  • Population 2:<\/strong>\u00a0This population shows a pattern of\u00a0linear decay<\/strong>. It decreases by a constant amount of 2 thousand sloths each year (e.g., 39 – 2 = 37; 37 – 2 = 35).<\/li>\n<\/ul>\n\n\n\n

    b. These patterns continued for many years. Based on this information, fill in the extra rows in the table.<\/strong><\/h3>\n\n\n\n

    Using the patterns identified in part a, we can complete the table.<\/p>\n\n\n\n

      \n
    • For Population 1, we multiply the previous year’s value by 0.85.<\/li>\n\n\n\n
    • For Population 2, we subtract 2 from the previous year’s value.<\/li>\n<\/ul>\n\n\n\n
      time (years since 1990)<\/td>population 1 (thousands)<\/td>population 2 (thousands)<\/td><\/tr>
      0<\/td>90.0<\/td>39<\/td><\/tr>
      1<\/td>76.5<\/td>37<\/td><\/tr>
      2<\/td>65.0<\/td>35<\/td><\/tr>
      3<\/td>55.3<\/td>33<\/td><\/tr>
      4<\/td>47.0<\/td>31<\/td><\/tr>
      5<\/td>39.9<\/strong><\/td>29<\/strong><\/td><\/tr>
      6<\/td>33.9<\/strong><\/td>27<\/strong><\/td><\/tr>
      7<\/td>28.9<\/strong><\/td>25<\/strong><\/td><\/tr>
      8<\/td>24.5<\/strong><\/td>23<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      (Calculations for Population 1 are rounded to one decimal place, e.g., 47.0 \u00d7 0.85 = 39.95 \u2248 39.9)<\/em><\/p>\n\n\n\n

      c. On the same axes, draw graphs of the two populations over time.<\/strong><\/h3>\n\n\n\n

      The graph would show “Time (years since 1990)” on the x-axis and “Population (thousands)” on the y-axis.<\/p>\n\n\n\n

        \n
      • Graph of Population 1:<\/strong>\u00a0This graph would be a downward-sloping\u00a0curve<\/strong>. It starts at (0, 90) and decreases sharply at first, then becomes less steep over time, which is characteristic of exponential decay.<\/li>\n\n\n\n
      • Graph of Population 2:<\/strong>\u00a0This graph would be a\u00a0straight line<\/strong>\u00a0that slopes downward. It starts at (0, 39) and decreases at a constant rate, passing through points like (4, 31) and (8, 23).<\/li>\n<\/ul>\n\n\n\n
        ![alt text](https:\/\/i.imgur.com\/gK6fDqg.png)<\/pre>\n\n\n\n
        d. Does Population 2 ever equal Population 1? If so, when? Explain or show your reasoning.<\/strong><\/h3>\n\n\n\n
        Yes, Population 2 will eventually equal Population 1.<\/p>\n\n\n\n
        Reasoning:<\/strong><\/p>\n\n\n\n
        We can determine this by continuing the pattern from the table for one more year.<\/p>\n\n\n\n
          \n
        • At\u00a0year 8<\/strong>:\n
            \n
          • Population 1 is\u00a024.5<\/strong>\u00a0thousand.<\/li>\n\n\n\n
          • Population 2 is\u00a023<\/strong>\u00a0thousand.<\/li>\n\n\n\n
          • At this point, Population 1 is still larger than Population 2.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • Let’s calculate for\u00a0year 9<\/strong>:\n
              \n
            • Population 1: 24.5 \u00d7 0.85 \u2248\u00a020.8<\/strong>\u00a0thousand.<\/li>\n\n\n\n
            • Population 2: 23 – 2 =\u00a021<\/strong>\u00a0thousand.<\/li>\n\n\n\n
            • At this point, Population 2 is now larger than Population 1.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
              Since Population 1 was larger at year 8 and Population 2 was larger at year 9, the two populations must have been equal at some point in time between year 8 and year 9<\/strong> (i.e., sometime during the year 1998).<\/p>\n\n\n\n
              \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
              The table shows two sloth populations growing over time. time population 1 population 2 (years since 1990) (thousands) (thousands) 0 90.0 39 1 76.5 37 2 65.0 35 3 55.3 33 4 47.0 31 5 6 7 8 a. Describe a pattern in how each population changed from one year to the next. b. These […]<\/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-232883","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232883","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=232883"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232883\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}