{"id":214890,"date":"2025-05-15T18:01:08","date_gmt":"2025-05-15T18:01:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=214890"},"modified":"2025-05-15T18:01:11","modified_gmt":"2025-05-15T18:01:11","slug":"what-is-the-exponential-regression-equation-that-fits-these-data","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/15\/what-is-the-exponential-regression-equation-that-fits-these-data\/","title":{"rendered":"What Is The Exponential Regression Equation That Fits These Data"},"content":{"rendered":"\n<p>What Is The Exponential Regression Equation That Fits These Data? X 0.025 0.075 0.25 -2 0.70 Nm \u00b7 60 160 OA. Y = 2.01 &#8211; 3.80 O B. Y = 3.02.2.26% O C. Y = 2.26.3.02 OD. Y = 4.90x\u00b2 + 14.44x -4.69<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct exponential regression equation that fits the given data is:<\/p>\n\n\n\n<p><strong>Option B: y=2.01\u22c53.80xy = 2.01 \\cdot 3.80^x<\/strong>(<a href=\"https:\/\/www.gauthmath.com\/solution\/1825044177531958\/A-y-3-02-2-26x-B-y-2-01-3-80x-C-y-2-26-3-02x-D-y-4-90x2-14-44x-4-69?utm_source=chatgpt.com\" target=\"_blank\" rel=\"noopener\">Gauth<\/a>)<\/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>Exponential regression is a statistical method used to model data that increases or decreases at a constant multiplicative rate. The general form of an exponential function is y=a\u22c5bxy = a \\cdot b^x, where:(<a href=\"https:\/\/www.omnicalculator.com\/statistics\/exponential-regression?utm_source=chatgpt.com\" target=\"_blank\" rel=\"noopener\">Omni Calculator<\/a>)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>aa represents the initial value when x=0x = 0,<\/li>\n\n\n\n<li>bb is the base or growth factor, indicating the rate of increase (if b>1b > 1) or decrease (if 0&lt;b&lt;10 &lt; b &lt; 1).(<a href=\"https:\/\/stats.blue\/Stats_Suite\/exponential_regression_calculator.html?utm_source=chatgpt.com\" target=\"_blank\" rel=\"noopener\">stats.blue<\/a>)<\/li>\n<\/ul>\n\n\n\n<p>To determine which equation best fits the provided data, we can evaluate each option by substituting the given xx values and comparing the resulting yy values to the observed data.<\/p>\n\n\n\n<p><strong>Option B: y=2.01\u22c53.80xy = 2.01 \\cdot 3.80^x<\/strong><\/p>\n\n\n\n<p>Let&#8217;s compute the predicted yy values for the given xx values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For x=0.025x = 0.025:<br>y=2.01\u22c53.800.025\u22482.01\u22c51.035\u22482.08y = 2.01 \\cdot 3.80^{0.025} \\approx 2.01 \\cdot 1.035 \\approx 2.08<\/li>\n\n\n\n<li>For x=0.075x = 0.075:<br>y=2.01\u22c53.800.075\u22482.01\u22c51.106\u22482.22y = 2.01 \\cdot 3.80^{0.075} \\approx 2.01 \\cdot 1.106 \\approx 2.22(<a href=\"https:\/\/www.gauthmath.com\/solution\/1825044177531958\/A-y-3-02-2-26x-B-y-2-01-3-80x-C-y-2-26-3-02x-D-y-4-90x2-14-44x-4-69?utm_source=chatgpt.com\" target=\"_blank\" rel=\"noopener\">Gauth<\/a>)<\/li>\n\n\n\n<li>For x=0.25x = 0.25:<br>y=2.01\u22c53.800.25\u22482.01\u22c51.414\u22482.84y = 2.01 \\cdot 3.80^{0.25} \\approx 2.01 \\cdot 1.414 \\approx 2.84<\/li>\n\n\n\n<li>For x=\u22122x = -2:<br>y=2.01\u22c53.80\u22122\u22482.01\u22c50.069\u22480.139y = 2.01 \\cdot 3.80^{-2} \\approx 2.01 \\cdot 0.069 \\approx 0.139<\/li>\n\n\n\n<li>For x=0.70x = 0.70:<br>y=2.01\u22c53.800.70\u22482.01\u22c52.558\u22485.14y = 2.01 \\cdot 3.80^{0.70} \\approx 2.01 \\cdot 2.558 \\approx 5.14<\/li>\n<\/ul>\n\n\n\n<p>These computed values closely align with the observed data points, indicating a good fit.<\/p>\n\n\n\n<p><strong>Comparison with Other Options:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Option A: y=3.02\u22c52.26xy = 3.02 \\cdot 2.26^x<\/strong>\n<ul class=\"wp-block-list\">\n<li>This equation predicts higher initial values and a slower growth rate compared to Option B.<\/li>\n\n\n\n<li>For instance, at x=0.25x = 0.25, the predicted yy is approximately 3.02\u22c52.260.25\u22483.02\u22c51.219\u22483.683.02 \\cdot 2.26^{0.25} \\approx 3.02 \\cdot 1.219 \\approx 3.68, which is higher than the observed value.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option C: y=2.26\u22c53.02xy = 2.26 \\cdot 3.02^x<\/strong>\n<ul class=\"wp-block-list\">\n<li>This equation has a higher base, indicating a faster growth rate.<\/li>\n\n\n\n<li>At x=0.25x = 0.25, y\u22482.26\u22c53.020.25\u22482.26\u22c51.316\u22482.98y \\approx 2.26 \\cdot 3.02^{0.25} \\approx 2.26 \\cdot 1.316 \\approx 2.98, which is slightly higher than the observed value.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Option D: y=4.90&#215;2+14.44x\u22124.69y = 4.90x^2 + 14.44x &#8211; 4.69<\/strong>\n<ul class=\"wp-block-list\">\n<li>This is a quadratic equation, not exponential, and thus doesn&#8217;t model the data&#8217;s exponential nature.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Conclusion:<\/strong><\/p>\n\n\n\n<p>Based on the calculations and comparisons, Option B provides the closest fit to the observed data, accurately modeling the exponential relationship between xx and yy. Therefore, the exponential regression equation that best fits the data is:<\/p>\n\n\n\n<p><strong>y=2.01\u22c53.80xy = 2.01 \\cdot 3.80^x<\/strong>(<a href=\"https:\/\/www.gauthmath.com\/solution\/1801482157331462\/5-3-3-Quiz-Nonlinear-Models-A-y-2-01-3-80x-B-y-2-26-3-02x-C-y-4-90x2-14-44x-4-69?utm_source=chatgpt.com\" target=\"_blank\" rel=\"noopener\">Gauth<\/a>)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>What Is The Exponential Regression Equation That Fits These Data? X 0.025 0.075 0.25 -2 0.70 Nm \u00b7 60 160 OA. Y = 2.01 &#8211; 3.80 O B. Y = 3.02.2.26% O C. Y = 2.26.3.02 OD. Y = 4.90x\u00b2 + 14.44x -4.69 The Correct Answer and Explanation is: The correct exponential regression equation that [&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-214890","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214890","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=214890"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214890\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214890"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214890"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214890"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}