{"id":491,"date":"2025-02-13T19:45:26","date_gmt":"2025-02-13T19:45:26","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/exponential-growth-and-decay-apply-it\/"},"modified":"2025-02-13T19:45:26","modified_gmt":"2025-02-13T19:45:26","slug":"exponential-growth-and-decay-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/exponential-growth-and-decay-apply-it\/","title":{"raw":"Exponential Growth and Decay: Apply It","rendered":"Exponential Growth and Decay: Apply It"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Apply the exponential growth formula to real-world cases like increasing populations or investments<\/li>\n\t<li>Describe how long it takes for quantities to double or reduce by half<\/li>\n\t<li>Implement the exponential decay formula for scenarios like radioactive substances decaying or objects cooling down<\/li>\n<\/ul>\n<\/section>\n<h2>Exponential Growth and Decay<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/M9rcYTuFG4w?si=IaDX4PV6vYgCzXIx\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/iT2tdp8Z0nY?si=Jajoi1ukMgycvhxM\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/R3sl_nT09H0?si=UUqj3uTHOiZXEwpL\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/xDoNxBG1J84?si=BP6EXHpVS8LQf4SO\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/ASV6vqyQEs0?si=utBu-c8Dhlw-pc7_\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/section>\n<em>Note: These videos use [latex]P[\/latex] and [latex]P_0[\/latex] where the text uses [latex]y[\/latex] and [latex]y_0[\/latex] in the exponential growth and decay equations. While the notation looks different, they are saying the same thing.<\/em>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Apply the exponential growth formula to real-world cases like increasing populations or investments<\/li>\n<li>Describe how long it takes for quantities to double or reduce by half<\/li>\n<li>Implement the exponential decay formula for scenarios like radioactive substances decaying or objects cooling down<\/li>\n<\/ul>\n<\/section>\n<h2>Exponential Growth and Decay<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/M9rcYTuFG4w?si=IaDX4PV6vYgCzXIx\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/iT2tdp8Z0nY?si=Jajoi1ukMgycvhxM\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/R3sl_nT09H0?si=UUqj3uTHOiZXEwpL\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/xDoNxBG1J84?si=BP6EXHpVS8LQf4SO\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/ASV6vqyQEs0?si=utBu-c8Dhlw-pc7_\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/section>\n<p><em>Note: These videos use [latex]P[\/latex] and [latex]P_0[\/latex] where the text uses [latex]y[\/latex] and [latex]y_0[\/latex] in the exponential growth and decay equations. While the notation looks different, they are saying the same thing.<\/em><\/p>\n","protected":false},"author":6,"menu_order":12,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":479,"module-header":"","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/491"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/491\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/479"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/491\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=491"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=491"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=491"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}