{"id":2658,"date":"2017-04-14T17:35:16","date_gmt":"2017-04-14T17:35:16","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=2658"},"modified":"2019-10-03T21:03:34","modified_gmt":"2019-10-03T21:03:34","slug":"assignment-growth-models-writing-task","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/chapter\/assignment-growth-models-writing-task\/","title":{"raw":"Assignment: Growth Models Writing Task","rendered":"Assignment: Growth Models Writing Task"},"content":{"raw":"<h3>Preparation<\/h3>\r\nSearch the Internet to find a graph or table of values that shows how something is changing over time.\u00a0 The data should be real measured data (not some made-up values for a math problem example or something), and should show something that is changing linear or exponentially.\r\n<ul>\r\n \t<li>The graph or table should show data for at least 4 time periods (years, months, etc.)<\/li>\r\n \t<li>Find data that appears to have a linear or exponential trend.<\/li>\r\n \t<li>Find data that someone hasn't already used.<\/li>\r\n<\/ul>\r\n<h3>What You Will Turn In<\/h3>\r\n<ul>\r\n \t<li>Construct a document that includes a link to the data or graph you used\u00a0(+2 pt for including, -10 for not including)<\/li>\r\n \t<li>Recreate the table (if it's huge, just include at least 4 time periods), or create a table from the graph you chose and include it in your document (6 pts.)<\/li>\r\n \t<li>State whether the data appears to be changing linearly or exponentially, and give a reason (4 pts)<\/li>\r\n \t<li>Find an explicit equation to model the data, clearly defining your variables and showing your work (10 pts)<\/li>\r\n \t<li>Use your model to make a prediction about the future (4 pts)<\/li>\r\n<\/ul>\r\n<h2><strong>Example<\/strong><\/h2>\r\n<a href=\"http:\/\/www.co.snohomish.wa.us\/Documents\/Departments\/Prosecuting_Attorney\/Statistics.pdf\" target=\"_blank\">Table 2 on page 2 of this document<\/a>\u00a0from Snohomish County, WA\u00a0shows the incidents of sexual orientation motivated hate crimes in Washington.\r\n\r\n1996\u00a0 1016\r\n1997\u00a0 1102\r\n1998\u00a0 1260\r\n1999\u00a0 1317\r\n2000\u00a0 1299\r\n2001\u00a0 1393\r\n\r\nWhile not perfectly linear, the trend appears roughly linear [don't just assume linearity! - make sure you can give a reason.\u00a0 If I graph your data and it looks exponential, you WILL lose points].\u00a0 Using the 1996 as n=0, and using data from 1996 and 2001,\r\n\r\n(1996)\u00a0 P<sub>0<\/sub> = 1016\r\n(2001)\u00a0 P<sub>5<\/sub> = 1393\r\n\r\n[FROM HERE, you would then follow the examples in the book to calculate the equation.\u00a0 IF your data is changing linearly, the procedure will be similar to the \"population of elk\" example.\u00a0 IF your data is changing exponentially, the procedure will be similar to the \"carbon dioxide emissions\" example.\u00a0\u00a0 Suppose I followed the procedure, showing my steps, and came up with this equation:]\r\n\r\nP<sub>n<\/sub> = 1016 + 75n\u00a0\u00a0 where n is years after 1996\r\n\r\nPredicting in 2010 (n=14):\r\n\r\nP<sub>14<\/sub> = 1016 + 75(14) = 2066\r\n\r\nSo if this trend were to continue at this rate, this model predicts that in 2010 there would be 2066 incidents of sexual orientation motivated hate crimes in Washington.\r\n\r\nAgain, this example was specific to linear growth.\u00a0 For an example using exponential growth, see the carbon dioxide emissions example in the book.\r\n\r\n-------------------------------------------------------------------\r\n<h3><strong>A note on determining if the trend is linear or exponential<\/strong><\/h3>\r\nLinear trends increase by approximately the same amount each year (or month or whatever the time unit is), so they have the shape of straight lines.\u00a0 It is important to remember, though, that the world is not perfect, so data is rarely a perfect line.\u00a0 The gas consumption example in the book is an example of data that is not perfectly in a linear, but appears to have an approximately linear trend; in other words, a line fits it pretty well.\r\n\r\nExponential trends are ones that increase by the same <em>percent<\/em> each year (or whatever the time unit is).\u00a0 If the data is increasing, they have a shape that curves upwards.\u00a0 Sometimes that curve upwards is subtle (like in the first graph of the fish population in the book), and sometimes it's very pronounced (like in the second graph of the fish population). If the data is a decreasing trend, an exponential trend would look something like this:<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21211822\/Screen-Shot-2016-12-21-at-4.17.58-PM.png\"><img class=\"aligncenter size-full wp-image-938\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21211822\/Screen-Shot-2016-12-21-at-4.17.58-PM.png\" alt=\"Generic graph showing increments of 1, from 0-5, vertically; increments of 1, 0-10, horizontally. The line slopes down to the left, curved.\" width=\"312\" height=\"159\" \/><\/a>\r\n\r\nIn some cases, it's hard to tell if the trend is linear or exponential.\u00a0 In that case, think about how the quantity is changing.\u00a0 Is it likely to be increasing by the same <em>number<\/em> each year?\u00a0 Or is likely to be increasing by the same <em>percent<\/em> each year?\r\n\r\nKeep in mind that there's always a third possibility:\u00a0 that the data is not changing linearly <em>or<\/em> exponentially.\u00a0 Here's a great example:<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21212502\/usa2.gif\"><img class=\"aligncenter size-full wp-image-939\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21212502\/usa2.gif\" alt=\"Graph titled \u201cUSA\u201d. Vertical left measures Billion (constant 2005 USD), in increments of 2000 from 0 to 14000. Horizontal measures years, in increments of 2 from 1998 to 2010. Vertical right measures Billion (constant 2009 USD) in increments of 100 from 0 to 800. A blue line (labeled \u201cGDP (left axis)\u201d) moves slowly up to the right, with some troughs and peaks. A red line (labeled \u201cMilitary expenditure (right axis)\u201d) swings from mid-point, down, and curves back up again to the right. \" width=\"468\" height=\"351\" \/><\/a>\r\n\r\nIn this graph, the blue graph looks approximately linear, but the red graph is <em>neither<\/em> linear or exponential (and you shouldn't use data like that for this assignment!)\r\n<p class=\"p1\"><\/p>\r\n<p class=\"p1\"><\/p>\r\n<p class=\"p1\">Download the assignment from one of the links below (.docx or .rtf):<\/p>\r\n<p class=\"p2\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/WM+Math+For+Liberal+Arts\/Growth+Models+Writing+Task.docx\">Growth Models Writing Task: Word Document<\/a><\/p>\r\n<p class=\"p2\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/WM+Math+For+Liberal+Arts\/Growth+Models+Writing+Task.rtf\">Growth Models Writing Task: Rich Text Format<\/a><\/p>","rendered":"<h3>Preparation<\/h3>\n<p>Search the Internet to find a graph or table of values that shows how something is changing over time.\u00a0 The data should be real measured data (not some made-up values for a math problem example or something), and should show something that is changing linear or exponentially.<\/p>\n<ul>\n<li>The graph or table should show data for at least 4 time periods (years, months, etc.)<\/li>\n<li>Find data that appears to have a linear or exponential trend.<\/li>\n<li>Find data that someone hasn&#8217;t already used.<\/li>\n<\/ul>\n<h3>What You Will Turn In<\/h3>\n<ul>\n<li>Construct a document that includes a link to the data or graph you used\u00a0(+2 pt for including, -10 for not including)<\/li>\n<li>Recreate the table (if it&#8217;s huge, just include at least 4 time periods), or create a table from the graph you chose and include it in your document (6 pts.)<\/li>\n<li>State whether the data appears to be changing linearly or exponentially, and give a reason (4 pts)<\/li>\n<li>Find an explicit equation to model the data, clearly defining your variables and showing your work (10 pts)<\/li>\n<li>Use your model to make a prediction about the future (4 pts)<\/li>\n<\/ul>\n<h2><strong>Example<\/strong><\/h2>\n<p><a href=\"http:\/\/www.co.snohomish.wa.us\/Documents\/Departments\/Prosecuting_Attorney\/Statistics.pdf\" target=\"_blank\">Table 2 on page 2 of this document<\/a>\u00a0from Snohomish County, WA\u00a0shows the incidents of sexual orientation motivated hate crimes in Washington.<\/p>\n<p>1996\u00a0 1016<br \/>\n1997\u00a0 1102<br \/>\n1998\u00a0 1260<br \/>\n1999\u00a0 1317<br \/>\n2000\u00a0 1299<br \/>\n2001\u00a0 1393<\/p>\n<p>While not perfectly linear, the trend appears roughly linear [don&#8217;t just assume linearity! &#8211; make sure you can give a reason.\u00a0 If I graph your data and it looks exponential, you WILL lose points].\u00a0 Using the 1996 as n=0, and using data from 1996 and 2001,<\/p>\n<p>(1996)\u00a0 P<sub>0<\/sub> = 1016<br \/>\n(2001)\u00a0 P<sub>5<\/sub> = 1393<\/p>\n<p>[FROM HERE, you would then follow the examples in the book to calculate the equation.\u00a0 IF your data is changing linearly, the procedure will be similar to the &#8220;population of elk&#8221; example.\u00a0 IF your data is changing exponentially, the procedure will be similar to the &#8220;carbon dioxide emissions&#8221; example.\u00a0\u00a0 Suppose I followed the procedure, showing my steps, and came up with this equation:]<\/p>\n<p>P<sub>n<\/sub> = 1016 + 75n\u00a0\u00a0 where n is years after 1996<\/p>\n<p>Predicting in 2010 (n=14):<\/p>\n<p>P<sub>14<\/sub> = 1016 + 75(14) = 2066<\/p>\n<p>So if this trend were to continue at this rate, this model predicts that in 2010 there would be 2066 incidents of sexual orientation motivated hate crimes in Washington.<\/p>\n<p>Again, this example was specific to linear growth.\u00a0 For an example using exponential growth, see the carbon dioxide emissions example in the book.<\/p>\n<p>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<\/p>\n<h3><strong>A note on determining if the trend is linear or exponential<\/strong><\/h3>\n<p>Linear trends increase by approximately the same amount each year (or month or whatever the time unit is), so they have the shape of straight lines.\u00a0 It is important to remember, though, that the world is not perfect, so data is rarely a perfect line.\u00a0 The gas consumption example in the book is an example of data that is not perfectly in a linear, but appears to have an approximately linear trend; in other words, a line fits it pretty well.<\/p>\n<p>Exponential trends are ones that increase by the same <em>percent<\/em> each year (or whatever the time unit is).\u00a0 If the data is increasing, they have a shape that curves upwards.\u00a0 Sometimes that curve upwards is subtle (like in the first graph of the fish population in the book), and sometimes it&#8217;s very pronounced (like in the second graph of the fish population). If the data is a decreasing trend, an exponential trend would look something like this:<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21211822\/Screen-Shot-2016-12-21-at-4.17.58-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-938\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21211822\/Screen-Shot-2016-12-21-at-4.17.58-PM.png\" alt=\"Generic graph showing increments of 1, from 0-5, vertically; increments of 1, 0-10, horizontally. The line slopes down to the left, curved.\" width=\"312\" height=\"159\" \/><\/a><\/p>\n<p>In some cases, it&#8217;s hard to tell if the trend is linear or exponential.\u00a0 In that case, think about how the quantity is changing.\u00a0 Is it likely to be increasing by the same <em>number<\/em> each year?\u00a0 Or is likely to be increasing by the same <em>percent<\/em> each year?<\/p>\n<p>Keep in mind that there&#8217;s always a third possibility:\u00a0 that the data is not changing linearly <em>or<\/em> exponentially.\u00a0 Here&#8217;s a great example:<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21212502\/usa2.gif\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-939\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21212502\/usa2.gif\" alt=\"Graph titled \u201cUSA\u201d. Vertical left measures Billion (constant 2005 USD), in increments of 2000 from 0 to 14000. Horizontal measures years, in increments of 2 from 1998 to 2010. Vertical right measures Billion (constant 2009 USD) in increments of 100 from 0 to 800. A blue line (labeled \u201cGDP (left axis)\u201d) moves slowly up to the right, with some troughs and peaks. A red line (labeled \u201cMilitary expenditure (right axis)\u201d) swings from mid-point, down, and curves back up again to the right.\" width=\"468\" height=\"351\" \/><\/a><\/p>\n<p>In this graph, the blue graph looks approximately linear, but the red graph is <em>neither<\/em> linear or exponential (and you shouldn&#8217;t use data like that for this assignment!)<\/p>\n<p class=\"p1\">\n<p class=\"p1\">\n<p class=\"p1\">Download the assignment from one of the links below (.docx or .rtf):<\/p>\n<p class=\"p2\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/WM+Math+For+Liberal+Arts\/Growth+Models+Writing+Task.docx\">Growth Models Writing Task: Word Document<\/a><\/p>\n<p class=\"p2\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/WM+Math+For+Liberal+Arts\/Growth+Models+Writing+Task.rtf\">Growth Models Writing Task: Rich Text Format<\/a><\/p>\n","protected":false},"author":17533,"menu_order":7,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2658","chapter","type-chapter","status-publish","hentry"],"part":356,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/2658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/2658\/revisions"}],"predecessor-version":[{"id":2803,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/2658\/revisions\/2803"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/parts\/356"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/2658\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/media?parent=2658"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapter-type?post=2658"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/contributor?post=2658"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/wp-json\/wp\/v2\/license?post=2658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}