{"id":669,"date":"2017-04-15T05:44:51","date_gmt":"2017-04-15T05:44:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/?post_type=chapter&#038;p=669"},"modified":"2019-06-26T19:15:14","modified_gmt":"2019-06-26T19:15:14","slug":"introduction-exponential-relationships","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/chapter\/introduction-exponential-relationships\/","title":{"raw":"Introduction to Exponential Relationships","rendered":"Introduction to Exponential Relationships"},"content":{"raw":"<h2>What you'll learn to do: Use an exponential model (when appropriate) to describe the relationship between two quantitative variables. Interpret the model in context.<\/h2>\r\nA common nonlinear model that occurs in real life is an exponential model, which is characterized by having a constant factor (or multiplier) for each constant increase in the dependent variable.\u00a0 Visually, the scatterplot of an exponential relationship should roughly follow a curve of one of these two shapes:\r\n\r\n<img class=\"alignleft wp-image-1903\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/26172933\/Exponential-Growth-Final-1024x1024.png\" alt=\"This is an example of an exponential growth graph that shows the red line curving up and to the right. It was created with Desmos and Spark Adobe.\" width=\"200\" height=\"200\" \/><img class=\"alignright wp-image-1905\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/26174323\/Exponential-Decay-Final1-300x300.png\" alt=\"This is an example of an exponential decay graph that shows the red line from the upper left moving down and to the right. It was created with Desmos and Spark Adobe.\" width=\"200\" height=\"200\" \/>\r\n<h2>Contribute!<\/h2><div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div><a href=\"https:\/\/docs.google.com\/document\/d\/13CzMIpuZihMEXhTFn_dueiZHgHGXjnD-wuHkmwZukjk\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a>","rendered":"<h2>What you&#8217;ll learn to do: Use an exponential model (when appropriate) to describe the relationship between two quantitative variables. Interpret the model in context.<\/h2>\n<p>A common nonlinear model that occurs in real life is an exponential model, which is characterized by having a constant factor (or multiplier) for each constant increase in the dependent variable.\u00a0 Visually, the scatterplot of an exponential relationship should roughly follow a curve of one of these two shapes:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1903\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/26172933\/Exponential-Growth-Final-1024x1024.png\" alt=\"This is an example of an exponential growth graph that shows the red line curving up and to the right. It was created with Desmos and Spark Adobe.\" width=\"200\" height=\"200\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-1905\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/26174323\/Exponential-Decay-Final1-300x300.png\" alt=\"This is an example of an exponential decay graph that shows the red line from the upper left moving down and to the right. It was created with Desmos and Spark Adobe.\" width=\"200\" height=\"200\" \/><\/p>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/13CzMIpuZihMEXhTFn_dueiZHgHGXjnD-wuHkmwZukjk\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-669\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\">http:\/\/oli.cmu.edu<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":163,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"35509f10-cffa-479f-b6f3-dcb9a7381137","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-669","chapter","type-chapter","status-publish","hentry"],"part":225,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/669","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":20,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/669\/revisions"}],"predecessor-version":[{"id":1919,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/669\/revisions\/1919"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/225"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/669\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=669"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=669"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=669"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}