{"id":3417,"date":"2024-06-24T16:34:30","date_gmt":"2024-06-24T16:34:30","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3417"},"modified":"2024-08-05T12:44:13","modified_gmt":"2024-08-05T12:44:13","slug":"derivatives-as-rates-of-change-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/chapter\/derivatives-as-rates-of-change-apply-it\/","title":{"raw":"Derivatives as Rates of Change: Apply It","rendered":"Derivatives as Rates of Change: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Calculate how quantities change on average over time<\/li>\r\n\t<li>Use rates of change to figure out how an object\u2019s position, speed, and acceleration are changing over time<\/li>\r\n\t<li>Estimate future population sizes using current data and how fast the population is growing<\/li>\r\n\t<li>Use derivatives to determine the cost and revenue of producing one more unit in a business<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 class=\"font-600 text-lg font-bold\">Rate of Change Applications in Real-World Scenarios<\/h2>\r\n<p class=\"whitespace-pre-wrap break-words\">In this Apply-It task, you'll explore how the Amount of Change Formula and related concepts can be applied to various real-world situations, including motion analysis, population growth, and business economics.<\/p>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288228[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288229[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288230[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288231[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288232[\/ohm_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate how quantities change on average over time<\/li>\n<li>Use rates of change to figure out how an object\u2019s position, speed, and acceleration are changing over time<\/li>\n<li>Estimate future population sizes using current data and how fast the population is growing<\/li>\n<li>Use derivatives to determine the cost and revenue of producing one more unit in a business<\/li>\n<\/ul>\n<\/section>\n<h2 class=\"font-600 text-lg font-bold\">Rate of Change Applications in Real-World Scenarios<\/h2>\n<p class=\"whitespace-pre-wrap break-words\">In this Apply-It task, you&#8217;ll explore how the Amount of Change Formula and related concepts can be applied to various real-world situations, including motion analysis, population growth, and business economics.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288228\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288228&theme=lumen&iframe_resize_id=ohm288228&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288229\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288229&theme=lumen&iframe_resize_id=ohm288229&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288230\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288230&theme=lumen&iframe_resize_id=ohm288230&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288231\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288231&theme=lumen&iframe_resize_id=ohm288231&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288232\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288232&theme=lumen&iframe_resize_id=ohm288232&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br 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