{"id":3152,"date":"2025-08-15T22:19:31","date_gmt":"2025-08-15T22:19:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=3152"},"modified":"2025-09-08T19:50:41","modified_gmt":"2025-09-08T19:50:41","slug":"application-of-rational-functions-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/application-of-rational-functions-apply-it\/","title":{"raw":"Applications of Rational Functions: Apply It","rendered":"Applications of Rational Functions: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Solve applied problems involving rational functions.<\/li>\r\n \t<li>Solve rational inequalities.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Home Solar Panel Efficiency Analysis<\/h2>\r\n<p class=\"whitespace-normal break-words\">Jake recently installed a solar panel system on his Phoenix home and wants to optimize its performance. His daily energy efficiency [latex]E(h)[\/latex] (as a percentage of maximum theoretical output) depends on the number of peak sunlight hours [latex]h[\/latex] according to:<\/p>\r\n<p class=\"whitespace-normal break-words\">[latex]E(h) = \\frac{90h - 180}{h + 4}[\/latex]<\/p>\r\n\r\n<h3 class=\"text-lg font-bold text-text-100 mt-1 -mb-1.5\">Solar Efficiency Analysis<\/h3>\r\n<p class=\"whitespace-normal break-words\">Jake's goal is to achieve at least 60% efficiency to make his monthly electricity bill negative (meaning he sells more energy back to the grid than he uses). This means he needs to solve the rational inequality:<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]311234[\/ohm_question]<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\">\r\n<p class=\"whitespace-normal break-words\"><strong>How to<\/strong>: To test signs in rational inequalities:<\/p>\r\n\r\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\">Pick a test point from each relevant interval<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Substitute into the simplified expression<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Determine if the result is positive or negative<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Include intervals where the expression satisfies the inequality<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]311235[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Solve applied problems involving rational functions.<\/li>\n<li>Solve rational inequalities.<\/li>\n<\/ul>\n<\/section>\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Home Solar Panel Efficiency Analysis<\/h2>\n<p class=\"whitespace-normal break-words\">Jake recently installed a solar panel system on his Phoenix home and wants to optimize its performance. His daily energy efficiency [latex]E(h)[\/latex] (as a percentage of maximum theoretical output) depends on the number of peak sunlight hours [latex]h[\/latex] according to:<\/p>\n<p class=\"whitespace-normal break-words\">[latex]E(h) = \\frac{90h - 180}{h + 4}[\/latex]<\/p>\n<h3 class=\"text-lg font-bold text-text-100 mt-1 -mb-1.5\">Solar Efficiency Analysis<\/h3>\n<p class=\"whitespace-normal break-words\">Jake&#8217;s goal is to achieve at least 60% efficiency to make his monthly electricity bill negative (meaning he sells more energy back to the grid than he uses). This means he needs to solve the rational inequality:<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm311234\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=311234&theme=lumen&iframe_resize_id=ohm311234&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\">\n<p class=\"whitespace-normal break-words\"><strong>How to<\/strong>: To test signs in rational inequalities:<\/p>\n<ol class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\">Pick a test point from each relevant interval<\/li>\n<li class=\"whitespace-normal break-words\">Substitute into the simplified expression<\/li>\n<li class=\"whitespace-normal break-words\">Determine if the result is positive or negative<\/li>\n<li class=\"whitespace-normal break-words\">Include intervals where the expression satisfies the inequality<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm311235\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=311235&theme=lumen&iframe_resize_id=ohm311235&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":67,"menu_order":18,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":508,"module-header":"apply_it","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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3152"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3152\/revisions"}],"predecessor-version":[{"id":3800,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3152\/revisions\/3800"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/508"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3152\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=3152"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=3152"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=3152"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=3152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}