{"id":293,"date":"2024-10-18T21:23:32","date_gmt":"2024-10-18T21:23:32","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/modeling-exponential-growth-apply-it-1\/"},"modified":"2024-10-18T21:23:54","modified_gmt":"2024-10-18T21:23:54","slug":"modeling-exponential-growth-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/modeling-exponential-growth-apply-it-1\/","title":{"raw":"Modeling Exponential Growth: Apply It 1","rendered":"Modeling Exponential Growth: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Perform exponential regression<\/li>\r\n \t<li>Convert between exponential and continuous growth<\/li>\r\n \t<li>Compare exponential and linear regressions for best fit<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Mastering Exponential Growth and Regression Analysis<\/h2>\r\nIn this 'Apply It' activity, we venture into the realm of exponential growth and regression analysis, crucial tools for understanding and predicting trends in diverse fields. You will encounter two scenarios: the growth of a tech startup and the environmental impact of CO<sub>2<\/sub> emissions. These scenarios will challenge you to perform and compare different types of regression analyses, including exponential and linear models, as well as to understand the nuances between exponential and continuous growth models. This exercise aims to deepen your comprehension of how mathematical modeling can be applied to interpret complex real-world data.\r\n<h3>Scenario 1: Tech Startup Growth<\/h3>\r\nA tech startup has been tracking its monthly revenue over the past two years. The data suggests exponential growth.\r\n<table style=\"margin-left: auto; margin-right: auto; text-align: center; width: 50%; height: 550px;\" border=\"1\">\r\n<tbody>\r\n<tr style=\"height: 22px;\">\r\n<th style=\"height: 22px;\">Month<\/th>\r\n<th style=\"height: 22px;\">Revenue (in thousands)<\/th>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">1<\/td>\r\n<td style=\"height: 22px;\">[latex]15[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">2<\/td>\r\n<td style=\"height: 22px;\">[latex]18[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">3<\/td>\r\n<td style=\"height: 22px;\">[latex]22[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">4<\/td>\r\n<td style=\"height: 22px;\">[latex]28[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">5<\/td>\r\n<td style=\"height: 22px;\">[latex]31[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">6<\/td>\r\n<td style=\"height: 22px;\">[latex]37[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">7<\/td>\r\n<td style=\"height: 22px;\">[latex]44[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">8<\/td>\r\n<td style=\"height: 22px;\">[latex]52[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">9<\/td>\r\n<td style=\"height: 22px;\">[latex]65[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">10<\/td>\r\n<td style=\"height: 22px;\">[latex]78[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">11<\/td>\r\n<td style=\"height: 22px;\">[latex]88[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">12<\/td>\r\n<td style=\"height: 22px;\">[latex]105[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">13<\/td>\r\n<td style=\"height: 22px;\">[latex]125[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">14<\/td>\r\n<td style=\"height: 22px;\">[latex]149[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">15<\/td>\r\n<td style=\"height: 22px;\">[latex]178[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">16<\/td>\r\n<td style=\"height: 22px;\">[latex]225[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">17<\/td>\r\n<td style=\"height: 22px;\">[latex]253[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">18<\/td>\r\n<td style=\"height: 22px;\">[latex]302[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">19<\/td>\r\n<td style=\"height: 22px;\">[latex]360[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">20<\/td>\r\n<td style=\"height: 22px;\">[latex]429[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">21<\/td>\r\n<td style=\"height: 22px;\">[latex]499[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">22<\/td>\r\n<td style=\"height: 22px;\">[latex]610[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">23<\/td>\r\n<td style=\"height: 22px;\">[latex]728[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 22px;\">\r\n<td style=\"height: 22px;\">24<\/td>\r\n<td style=\"height: 22px;\">[latex]810[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]13943[\/ohm2_question]\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Perform exponential regression<\/li>\n<li>Convert between exponential and continuous growth<\/li>\n<li>Compare exponential and linear regressions for best fit<\/li>\n<\/ul>\n<\/section>\n<h2>Mastering Exponential Growth and Regression Analysis<\/h2>\n<p>In this &#8216;Apply It&#8217; activity, we venture into the realm of exponential growth and regression analysis, crucial tools for understanding and predicting trends in diverse fields. You will encounter two scenarios: the growth of a tech startup and the environmental impact of CO<sub>2<\/sub> emissions. These scenarios will challenge you to perform and compare different types of regression analyses, including exponential and linear models, as well as to understand the nuances between exponential and continuous growth models. This exercise aims to deepen your comprehension of how mathematical modeling can be applied to interpret complex real-world data.<\/p>\n<h3>Scenario 1: Tech Startup Growth<\/h3>\n<p>A tech startup has been tracking its monthly revenue over the past two years. The data suggests exponential growth.<\/p>\n<table style=\"margin-left: auto; margin-right: auto; text-align: center; width: 50%; height: 550px;\">\n<tbody>\n<tr style=\"height: 22px;\">\n<th style=\"height: 22px;\">Month<\/th>\n<th style=\"height: 22px;\">Revenue (in thousands)<\/th>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">1<\/td>\n<td style=\"height: 22px;\">[latex]15[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">2<\/td>\n<td style=\"height: 22px;\">[latex]18[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">3<\/td>\n<td style=\"height: 22px;\">[latex]22[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">4<\/td>\n<td style=\"height: 22px;\">[latex]28[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">5<\/td>\n<td style=\"height: 22px;\">[latex]31[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">6<\/td>\n<td style=\"height: 22px;\">[latex]37[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">7<\/td>\n<td style=\"height: 22px;\">[latex]44[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">8<\/td>\n<td style=\"height: 22px;\">[latex]52[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">9<\/td>\n<td style=\"height: 22px;\">[latex]65[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">10<\/td>\n<td style=\"height: 22px;\">[latex]78[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">11<\/td>\n<td style=\"height: 22px;\">[latex]88[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">12<\/td>\n<td style=\"height: 22px;\">[latex]105[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">13<\/td>\n<td style=\"height: 22px;\">[latex]125[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">14<\/td>\n<td style=\"height: 22px;\">[latex]149[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">15<\/td>\n<td style=\"height: 22px;\">[latex]178[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">16<\/td>\n<td style=\"height: 22px;\">[latex]225[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">17<\/td>\n<td style=\"height: 22px;\">[latex]253[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">18<\/td>\n<td style=\"height: 22px;\">[latex]302[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">19<\/td>\n<td style=\"height: 22px;\">[latex]360[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">20<\/td>\n<td style=\"height: 22px;\">[latex]429[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">21<\/td>\n<td style=\"height: 22px;\">[latex]499[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">22<\/td>\n<td style=\"height: 22px;\">[latex]610[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">23<\/td>\n<td style=\"height: 22px;\">[latex]728[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 22px;\">\n<td style=\"height: 22px;\">24<\/td>\n<td style=\"height: 22px;\">[latex]810[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm13943\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13943&theme=lumen&iframe_resize_id=ohm13943&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":6,"menu_order":13,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":266,"module-header":"- Select Header 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