{"id":5418,"date":"2021-01-27T17:45:40","date_gmt":"2021-01-27T17:45:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/?post_type=chapter&#038;p=5418"},"modified":"2025-11-30T03:22:54","modified_gmt":"2025-11-30T03:22:54","slug":"3-4-comparing-linear-and-exponential-models","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/3-4-comparing-linear-and-exponential-models\/","title":{"raw":"3.4 Comparing Linear and Exponential Models","rendered":"3.4 Comparing Linear and Exponential Models"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Determine the difference between linear and exponential growth.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Linear Growth<\/h3>\r\nStudy the double number line below. On the bottom of the number line is the number of gallons put into the car. The top of the number line is the price the customer pays. For each gallon of gas put into the car, $2.25 is added to the price the customer has to pay.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07021947\/Double-Number-Line-1.jpg\"><img class=\"alignnone wp-image-5635\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07021947\/Double-Number-Line-1.jpg\" alt=\"\" width=\"840\" height=\"224\" \/><\/a>\r\n\r\nInstead of adding $2.25 over and over (repeated addition), we use multiplication. The price the customer has to pay is $2.25 times the number of gallons of gasoline put into the car. The linear growth model represented by the above double number line is:\r\n<p style=\"text-align: center;\"><strong>y = 2.25x<\/strong>, where y is the price the customer owes and x is the number of gallons<\/p>\r\n\r\n<h3>Exponential Growth<\/h3>\r\nNow, consider the double number line below. On the bottom of the number line is the number of years of an investment.\u00a0 The top of the number line is the accumulated amount in the investment. The initial investment was $100. Each year, the amount in the account was multiplied by 1.05. The 1.05 tells us the investment grew 5% each year.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07022024\/Double-Number-Line-2.jpg\"><img class=\"alignnone wp-image-5636\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07022024\/Double-Number-Line-2.jpg\" alt=\"\" width=\"852\" height=\"213\" \/><\/a>\r\n\r\nInstead of multiplying by 1.05 over and over (repeated multiplication), we use exponents. The base (or growth factor) of 1.05 is multiplied by the investment amount each year. The exponential growth model represented by the above double number line is:\r\n<p style=\"text-align: center;\"><strong>y = 100 (1.05)<sup>x<\/sup><\/strong>, where y is the amount accumulated in the investment and x is the number of years<\/p>\r\n\r\n<h3>Comparing Linear and Exponential Growth<\/h3>\r\nOne way to determine if a model is linear or exponential, is to examine the graphs.\r\n<table style=\"border-collapse: collapse; width: 100%; height: 433px;\" border=\"1\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; text-align: center; height: 14px;\"><strong>Linear Growth<\/strong><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 14px;\"><strong>Exponential Growth<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 419px;\">\r\n<td style=\"width: 50%; text-align: center; height: 419px;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07024800\/Line-2.jpg\"><img class=\"alignnone wp-image-5642\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07024800\/Line-2-295x300.jpg\" alt=\"\" width=\"378\" height=\"385\" \/><\/a><\/td>\r\n<td style=\"width: 50%; text-align: center; height: 419px;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07024837\/Expo-21.jpg\"><img class=\"alignnone wp-image-5643\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07024837\/Expo-21-300x300.jpg\" alt=\"\" width=\"365\" height=\"365\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAnother way to determine if a model is linear or exponential is to examine the table of values.\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\">In a <strong>linear model<\/strong>, each time x is increased by one, the same number is <strong>added<\/strong> to the y-value.<\/td>\r\n<td style=\"width: 50%;\">In an <strong>exponential model<\/strong>, each time x is increased by one, the same number is <strong>multiplied<\/strong> by the y-value.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07031116\/Linear-Table-1.jpg\"><img class=\"alignnone size-medium wp-image-5645\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07031116\/Linear-Table-1-300x283.jpg\" alt=\"\" width=\"300\" height=\"283\" \/><\/a><\/td>\r\n<td style=\"width: 50%; text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07031409\/Expo-Table-2.jpg\"><img class=\"alignnone size-medium wp-image-5646\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07031409\/Expo-Table-2-300x286.jpg\" alt=\"\" width=\"300\" height=\"286\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nFor each model below, determine if it is linear or exponential growth. Then write the equation that models the growth.\r\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 37.5051%;\"><strong>\u00a0\u00a0\u00a0\u00a0 Model 1<\/strong><\/td>\r\n<td style=\"width: 37.3824%;\"><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Model 2<\/strong><\/td>\r\n<td style=\"width: 25.1124%;\"><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Model 3<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"border-collapse: collapse; width: 100%; height: 82px;\" border=\"1\">\r\n<tbody>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>x<\/strong><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>y<\/strong><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>x<\/strong><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>y<\/strong><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>x<\/strong><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>y<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 10px;\">\r\n<td style=\"width: 12.5%; text-align: center; height: 10px;\">0<\/td>\r\n<td style=\"width: 12.5%; height: 10px; text-align: center;\">2<\/td>\r\n<td style=\"width: 12.5%; height: 10px;\"><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 10px;\">0<\/td>\r\n<td style=\"width: 12.5%; height: 10px; text-align: center;\">1<\/td>\r\n<td style=\"width: 12.5%; height: 10px;\"><\/td>\r\n<td style=\"width: 12.5%; height: 10px; text-align: center;\">0<\/td>\r\n<td style=\"width: 12.5%; height: 10px; text-align: center;\">7<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">1<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">10<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">1<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1.2<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">11<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">2<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">50<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">2<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1.44<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">2<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">15<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">3<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">250<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">3<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1.728<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">3<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">19<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">4<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1,250<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">4<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">2.0736<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">4<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">23<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">5<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">6,250<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">5<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">2.4883<\/td>\r\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">5<\/td>\r\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">27<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 37.5459%;\">[reveal-answer q=\"829358\"]Show Answer for Model 1[\/reveal-answer]\r\n[hidden-answer a=\"829358\"]Exponential; y = 2 (5)<sup>x[\/hidden-answer]<\/sup><\/td>\r\n<td style=\"width: 37.3454%;\">[reveal-answer q=\"568414\"]Show Answer for Model 2[\/reveal-answer]\r\n[hidden-answer a=\"568414\"] Exponential; y = 1 (1.2)<sup>x[\/hidden-answer]<\/sup><\/td>\r\n<td style=\"width: 25.1086%;\">[reveal-answer q=\"574841\"]Show Answer for Model 3[\/reveal-answer]\r\n[hidden-answer a=\"574841\"]Linear; y = 4x + 7[\/hidden-answer]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/strong><\/span><\/p>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Determine the difference between linear and exponential growth.<\/li>\n<\/ul>\n<\/div>\n<h3>Linear Growth<\/h3>\n<p>Study the double number line below. On the bottom of the number line is the number of gallons put into the car. The top of the number line is the price the customer pays. For each gallon of gas put into the car, $2.25 is added to the price the customer has to pay.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07021947\/Double-Number-Line-1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5635\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07021947\/Double-Number-Line-1.jpg\" alt=\"\" width=\"840\" height=\"224\" \/><\/a><\/p>\n<p>Instead of adding $2.25 over and over (repeated addition), we use multiplication. The price the customer has to pay is $2.25 times the number of gallons of gasoline put into the car. The linear growth model represented by the above double number line is:<\/p>\n<p style=\"text-align: center;\"><strong>y = 2.25x<\/strong>, where y is the price the customer owes and x is the number of gallons<\/p>\n<h3>Exponential Growth<\/h3>\n<p>Now, consider the double number line below. On the bottom of the number line is the number of years of an investment.\u00a0 The top of the number line is the accumulated amount in the investment. The initial investment was $100. Each year, the amount in the account was multiplied by 1.05. The 1.05 tells us the investment grew 5% each year.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07022024\/Double-Number-Line-2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5636\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07022024\/Double-Number-Line-2.jpg\" alt=\"\" width=\"852\" height=\"213\" \/><\/a><\/p>\n<p>Instead of multiplying by 1.05 over and over (repeated multiplication), we use exponents. The base (or growth factor) of 1.05 is multiplied by the investment amount each year. The exponential growth model represented by the above double number line is:<\/p>\n<p style=\"text-align: center;\"><strong>y = 100 (1.05)<sup>x<\/sup><\/strong>, where y is the amount accumulated in the investment and x is the number of years<\/p>\n<h3>Comparing Linear and Exponential Growth<\/h3>\n<p>One way to determine if a model is linear or exponential, is to examine the graphs.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 433px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; text-align: center; height: 14px;\"><strong>Linear Growth<\/strong><\/td>\n<td style=\"width: 50%; text-align: center; height: 14px;\"><strong>Exponential Growth<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 419px;\">\n<td style=\"width: 50%; text-align: center; height: 419px;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07024800\/Line-2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5642\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07024800\/Line-2-295x300.jpg\" alt=\"\" width=\"378\" height=\"385\" \/><\/a><\/td>\n<td style=\"width: 50%; text-align: center; height: 419px;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07024837\/Expo-21.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5643\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07024837\/Expo-21-300x300.jpg\" alt=\"\" width=\"365\" height=\"365\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Another way to determine if a model is linear or exponential is to examine the table of values.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">In a <strong>linear model<\/strong>, each time x is increased by one, the same number is <strong>added<\/strong> to the y-value.<\/td>\n<td style=\"width: 50%;\">In an <strong>exponential model<\/strong>, each time x is increased by one, the same number is <strong>multiplied<\/strong> by the y-value.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07031116\/Linear-Table-1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-5645\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07031116\/Linear-Table-1-300x283.jpg\" alt=\"\" width=\"300\" height=\"283\" \/><\/a><\/td>\n<td style=\"width: 50%; text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07031409\/Expo-Table-2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-5646\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/07031409\/Expo-Table-2-300x286.jpg\" alt=\"\" width=\"300\" height=\"286\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>For each model below, determine if it is linear or exponential growth. Then write the equation that models the growth.<\/p>\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 37.5051%;\"><strong>\u00a0\u00a0\u00a0\u00a0 Model 1<\/strong><\/td>\n<td style=\"width: 37.3824%;\"><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Model 2<\/strong><\/td>\n<td style=\"width: 25.1124%;\"><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Model 3<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border-collapse: collapse; width: 100%; height: 82px;\">\n<tbody>\n<tr style=\"height: 12px;\">\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>x<\/strong><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>y<\/strong><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>x<\/strong><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>y<\/strong><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>x<\/strong><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\"><strong>y<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 10px;\">\n<td style=\"width: 12.5%; text-align: center; height: 10px;\">0<\/td>\n<td style=\"width: 12.5%; height: 10px; text-align: center;\">2<\/td>\n<td style=\"width: 12.5%; height: 10px;\"><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 10px;\">0<\/td>\n<td style=\"width: 12.5%; height: 10px; text-align: center;\">1<\/td>\n<td style=\"width: 12.5%; height: 10px;\"><\/td>\n<td style=\"width: 12.5%; height: 10px; text-align: center;\">0<\/td>\n<td style=\"width: 12.5%; height: 10px; text-align: center;\">7<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">1<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">10<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">1<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1.2<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">11<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">2<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">50<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">2<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1.44<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">2<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">15<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">3<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">250<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">3<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1.728<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">3<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">19<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">4<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">1,250<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">4<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">2.0736<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">4<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">23<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">5<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">6,250<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; text-align: center; height: 12px;\">5<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">2.4883<\/td>\n<td style=\"width: 12.5%; height: 12px;\"><\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">5<\/td>\n<td style=\"width: 12.5%; height: 12px; text-align: center;\">27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 37.5459%;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q829358\">Show Answer for Model 1<\/span><\/p>\n<div id=\"q829358\" class=\"hidden-answer\" style=\"display: none\">Exponential; y = 2 (5)<sup>x<\/div>\n<\/div>\n<p><\/sup><\/td>\n<td style=\"width: 37.3454%;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q568414\">Show Answer for Model 2<\/span><\/p>\n<div id=\"q568414\" class=\"hidden-answer\" style=\"display: none\"> Exponential; y = 1 (1.2)<sup>x<\/div>\n<\/div>\n<p><\/sup><\/td>\n<td style=\"width: 25.1086%;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q574841\">Show Answer for Model 3<\/span><\/p>\n<div id=\"q574841\" class=\"hidden-answer\" style=\"display: none\">Linear; y = 4x + 7<\/div>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>This is the end of the section. 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