{"id":1413,"date":"2021-08-24T11:52:59","date_gmt":"2021-08-24T11:52:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1413"},"modified":"2022-01-31T21:35:00","modified_gmt":"2022-01-31T21:35:00","slug":"review-topics-for-success-5","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/review-topics-for-success-5\/","title":{"raw":"Review Topics for Success","rendered":"Review Topics for Success"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Identify and evaluate exponential functions<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Convert from logarithmic form to exponential form<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Convert from exponential form to logarithmic form<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Evaluate functions involving natural logarithms<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Apply the one-to-one property of exponents to solve an exponential equation<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Solve exponential equations of the form [latex]y=Ae^{kt} \\ \\mathrm{for} \\ t[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<img class=\"size-medium wp-image-1414 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/08\/24115203\/pexels-fabrizio-verrecchia-298018-300x199.jpg\" alt=\"a woman is facing a speeding train\" width=\"300\" height=\"199\" \/>Many discrete and continuous probability distributions involve exponential functions. An exponential function is a function involving a constant base and a variable exponent. Suppose you are waiting for a train, which is expected to come soon but might possibly arrive very late. You will learn to model waiting times using a continuous probability distribution. Since the graphs of certain exponential functions take on only positive values and decrease to nearly zero as the variable increases, they are helpful to model situations like wait times. Logarithms are a tool that we can use to solve exponential equations, so they will help us solve problems involving probability distributions modeled by exponential functions.\r\n<div class=\"textbox examples\">\r\n<h3>Recall for success<\/h3>\r\nLook for red boxes like this one throughout the text. They'll show up just in time to give helpful\u00a0reminders of the math you'll need, right where you'll need it.\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Identify and evaluate exponential functions<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Convert from logarithmic form to exponential form<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Convert from exponential form to logarithmic form<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Evaluate functions involving natural logarithms<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Apply the one-to-one property of exponents to solve an exponential equation<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Solve exponential equations of the form [latex]y=Ae^{kt} \\ \\mathrm{for} \\ t[\/latex]<\/li>\n<\/ul>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1414 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/08\/24115203\/pexels-fabrizio-verrecchia-298018-300x199.jpg\" alt=\"a woman is facing a speeding train\" width=\"300\" height=\"199\" \/>Many discrete and continuous probability distributions involve exponential functions. An exponential function is a function involving a constant base and a variable exponent. Suppose you are waiting for a train, which is expected to come soon but might possibly arrive very late. You will learn to model waiting times using a continuous probability distribution. Since the graphs of certain exponential functions take on only positive values and decrease to nearly zero as the variable increases, they are helpful to model situations like wait times. Logarithms are a tool that we can use to solve exponential equations, so they will help us solve problems involving probability distributions modeled by exponential functions.<\/p>\n<div class=\"textbox examples\">\n<h3>Recall for success<\/h3>\n<p>Look for red boxes like this one throughout the text. They&#8217;ll show up just in time to give helpful\u00a0reminders of the math you&#8217;ll need, right where you&#8217;ll need it.<\/p>\n<\/div>\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-1413\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Standing Woman Facing a Speeding Train. <strong>Authored by<\/strong>: Fabrizio Verrecchia. <strong>Provided by<\/strong>: Pexels. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.pexels.com\/photo\/standing-woman-facing-a-speeding-train-298018\/\">https:\/\/www.pexels.com\/photo\/standing-woman-facing-a-speeding-train-298018\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/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":169134,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Standing Woman Facing a Speeding Train\",\"author\":\"Fabrizio Verrecchia\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/standing-woman-facing-a-speeding-train-298018\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1413","chapter","type-chapter","status-publish","hentry"],"part":249,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1413\/revisions"}],"predecessor-version":[{"id":3598,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1413\/revisions\/3598"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/249"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1413\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1413"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1413"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1413"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}