{"id":230043,"date":"2025-06-08T18:58:29","date_gmt":"2025-06-08T18:58:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230043"},"modified":"2025-06-08T18:58:31","modified_gmt":"2025-06-08T18:58:31","slug":"yolanda-owns-4-rabbits","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/yolanda-owns-4-rabbits\/","title":{"rendered":"Yolanda owns 4 rabbits"},"content":{"rendered":"\n<p>Yolanda owns 4 rabbits. She expects the number of rabbits to double every year. b) write and equation to model this situation?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Equation:<\/h3>\n\n\n\n<p>To model the growth of the rabbit population, we use the formula for <strong>exponential growth<\/strong>:P(t)=P0\u22c52tP(t) = P_0 \\cdot 2^tP(t)=P0\u200b\u22c52t<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(t)P(t)P(t) is the number of rabbits after ttt years,<\/li>\n\n\n\n<li>P0P_0P0\u200b is the initial number of rabbits,<\/li>\n\n\n\n<li>ttt is the number of years,<\/li>\n\n\n\n<li>The base <strong>2<\/strong> represents the fact that the population <strong>doubles<\/strong> each year.<\/li>\n<\/ul>\n\n\n\n<p>Since Yolanda starts with 4 rabbits, P0=4P_0 = 4P0\u200b=4.<br>So, the equation becomes:P(t)=4\u22c52tP(t) = 4 \\cdot 2^tP(t)=4\u22c52t<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation <\/h3>\n\n\n\n<p>The situation described involves Yolanda starting with 4 rabbits and expecting the number of rabbits to <strong>double every year<\/strong>. This is a classic case of <strong>exponential growth<\/strong>, where the rate of increase is proportional to the current amount\u2014in this case, the number of rabbits.<\/p>\n\n\n\n<p>To write an equation modeling this situation, we start with the general exponential growth formula:P(t)=P0\u22c5rtP(t) = P_0 \\cdot r^tP(t)=P0\u200b\u22c5rt<\/p>\n\n\n\n<p>Here, P(t)P(t)P(t) is the population after ttt years, P0P_0P0\u200b is the starting number, and rrr is the growth rate. Since the number of rabbits doubles each year, the growth rate rrr is 2.<\/p>\n\n\n\n<p>Yolanda starts with 4 rabbits, so P0=4P_0 = 4P0\u200b=4. Substituting into the formula, we get:P(t)=4\u22c52tP(t) = 4 \\cdot 2^tP(t)=4\u22c52t<\/p>\n\n\n\n<p>This equation tells us how many rabbits Yolanda will have after any given number of years. For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After 1 year: P(1)=4\u22c521=8P(1) = 4 \\cdot 2^1 = 8P(1)=4\u22c521=8<\/li>\n\n\n\n<li>After 2 years: P(2)=4\u22c522=16P(2) = 4 \\cdot 2^2 = 16P(2)=4\u22c522=16<\/li>\n\n\n\n<li>After 3 years: P(3)=4\u22c523=32P(3) = 4 \\cdot 2^3 = 32P(3)=4\u22c523=32, and so on.<\/li>\n<\/ul>\n\n\n\n<p>The population keeps increasing faster over time because each year\u2019s growth builds upon the previous total. This type of growth is very different from <strong>linear growth<\/strong>, where the same number is added each year. Instead, exponential growth accelerates\u2014doubling the population every year means it grows very rapidly.<\/p>\n\n\n\n<p>This model assumes ideal conditions: no rabbits die, and there are enough resources to support unlimited growth. While not realistic over long periods, this equation is a good <strong>mathematical model<\/strong> for understanding the concept of doubling and exponential increase.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-719.jpeg\" alt=\"\" class=\"wp-image-230044\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Yolanda owns 4 rabbits. She expects the number of rabbits to double every year. b) write and equation to model this situation? The Correct Answer and Explanation is: Equation: To model the growth of the rabbit population, we use the formula for exponential growth:P(t)=P0\u22c52tP(t) = P_0 \\cdot 2^tP(t)=P0\u200b\u22c52t Where: Since Yolanda starts with 4 rabbits, [&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-230043","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230043","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=230043"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230043\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}