{"id":1965,"date":"2023-04-18T13:41:41","date_gmt":"2023-04-18T13:41:41","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=1965"},"modified":"2024-10-18T20:57:17","modified_gmt":"2024-10-18T20:57:17","slug":"linear-and-geometric-growth-fresh-take","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/linear-and-geometric-growth-fresh-take\/","title":{"raw":"Linear and Geometric Growth: Fresh Take","rendered":"Linear and Geometric Growth: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Identify whether a scenario or data describes linear or geometric growth<\/li>\r\n\t<li>Identify key growth parameters, such as growth rates and initial values, and express them in a format that can be used for calculation<\/li>\r\n\t<li>Use equations to predict future values for linear and exponential growth<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Predicting Growth<\/h2>\r\n<p>The steps of determining the formula and solving the problem of Marco\u2019s bottle collection shown on the Learn It page 1 are explained in detail in the following videos.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/SJcAjN-HL_I\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Linear+Growth+Part+1.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cLinear Growth Part 1\u201d here (opens in new window).<\/a><\/p>\r\n<p><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/4Two_oduhrA\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Linear+Growth+Part+2.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cLinear Growth Part 2\u201d here (opens in new window).<\/a><\/p>\r\n<p><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/pZ4u3j8Vmzo\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Linear+Growth+Part+3.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cLinear Growth Part 3\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Linear Growth<\/h2>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea<\/strong><\/p>\r\n<h4><strong>linear growth<\/strong><\/h4>\r\n<p>If a quantity starts at size [latex]P_0[\/latex]\u00a0and grows by [latex]d[\/latex] every time period, then the quantity after [latex]n[\/latex] time periods can be determined using either of these relations:<\/p>\r\n<p><strong>Recursive form<\/strong><\/p>\r\n<p style=\"text-align: center;\">[latex]P_n = P_{n-1} + d[\/latex]<\/p>\r\n<p><strong>Explicit form<\/strong><\/p>\r\n<p style=\"text-align: center;\">[latex]P_n = P_0 + d n[\/latex]<\/p>\r\n<p>In this equation, [latex]d[\/latex]\u00a0represents the <strong>common difference<\/strong> \u2013 the amount that the population changes each time [latex]n[\/latex] increases by [latex]1[\/latex].<\/p>\r\n<\/div>\r\n<section class=\"textbox example\">The cost, in dollars, of a gym membership for [latex]n[\/latex] months can be described by the explicit equation [latex]P_n = 70 + 30_n[\/latex]. What does this equation tell us?[reveal-answer q=\"438458\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"438458\"]The value for [latex]P_0[\/latex] in this equation is [latex]70[\/latex], so the initial starting cost is [latex]$70[\/latex]. This tells us that there must be an initiation or start-up fee of [latex]$70[\/latex] to join the gym.\r\n\r\n<p>The value for [latex]d[\/latex] in the equation is [latex]30[\/latex], so the cost increases by [latex]$30[\/latex] each month. This tells us that the monthly membership fee for the gym is [latex]$30[\/latex] a month.<\/p>\r\n<p>The explanation for this example is detailed below.<\/p>\r\n<p><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/0Uwz5dmLTtk?si=5UwcgQes_viYWnZ7\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Interpreting+a+linear+model.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cInterpreting a linear model\u201d here (opens in new window).<\/a><\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<h2>Exponential (Population) Growth<\/h2>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea<\/strong><\/p>\r\n<h4>exponential growth<\/h4>\r\n<p>If a quantity starts at size [latex]P_0[\/latex] and grows by [latex]R\\%[\/latex] (written as a decimal, [latex]r[\/latex]) every time period, then the quantity after [latex]n[\/latex] time periods can be determined using either of these relations:<\/p>\r\n<p><strong>Recursive form<\/strong><\/p>\r\n<p style=\"text-align: center;\">[latex]P_n = (1+r)P_{n-1}[\/latex]<\/p>\r\n<p><strong>Explicit form<\/strong><\/p>\r\n<p style=\"text-align: center;\">[latex]P_n = (1+r)^{n}P_0[\/latex]\u00a0 \u00a0 \u00a0 \u00a0 \u00a0or equivalently, [latex]P_n= P_0(1+r)^{n}[\/latex]<\/p>\r\n<p>We call\u00a0[latex]r[\/latex] the <strong>growth rate<\/strong>.<\/p>\r\n<p>The term\u00a0[latex](1+r)[\/latex] is called the <strong>growth multiplier<\/strong>, or common ratio.<\/p>\r\n<\/div>\r\n<section class=\"textbox example\">Between 2007 and 2008, Olympia, WA grew almost [latex]3\\%[\/latex] to a population of [latex]245[\/latex] thousand people. If this growth rate was to continue, what would the population of Olympia be in 2014?<br \/>\r\n[reveal-answer q=\"54756\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"54756\"]As we did before, we first need to define what year will correspond to [latex]n = 0[\/latex]. Since we know the population in 2008, it would make sense to have 2008 correspond to [latex]n = 0[\/latex], so [latex]P_0 = 245,000[\/latex]. The year 2014 would then be [latex]n = 6[\/latex]. We know the growth rate is [latex]3\\%[\/latex], giving [latex]r = 0.03[\/latex]. Using the explicit form:\r\n\r\n<p style=\"text-align: center;\">[latex]P_6 = (1+0.03)^{6}(245,000) = 1.19405(245,000) = 292,542.25[\/latex]<\/p>\r\n<p>The model predicts that in 2014, Olympia would have a population of about [latex]293[\/latex] thousand people.<\/p>\r\n<p>The following video explains this example in detail.<\/p>\r\n<p>https:\/\/youtu.be\/CDI4xS65rxY<\/p>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Predicting+future+population+using+an+exponential+model.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cPredicting future population using an exponential model\u201d here (opens in new window).<\/a><\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p>Watch the following videos for more on linear vs. exponential growth.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/_vlXdx-CqM0\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Examples+of+linear+and+exponential+relationships.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cExamples of linear and exponential relationships\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/8OHEgD6YMBw\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Understanding+linear+and+exponential+models+_+Functions+and+their+graphs+_+Algebra+II+_+Khan+Academy.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cUnderstanding linear and exponential models | Functions and their graphs | Algebra II | Khan Academy\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/721RrH6auoU\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Linear+vs.+exponential+growth_+from+data+_+High+School+Math+_+Khan+Academy.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cLinear vs. exponential growth: from data | High School Math | Khan Academy\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Identify whether a scenario or data describes linear or geometric growth<\/li>\n<li>Identify key growth parameters, such as growth rates and initial values, and express them in a format that can be used for calculation<\/li>\n<li>Use equations to predict future values for linear and exponential growth<\/li>\n<\/ul>\n<\/section>\n<h2>Predicting Growth<\/h2>\n<p>The steps of determining the formula and solving the problem of Marco\u2019s bottle collection shown on the Learn It page 1 are explained in detail in the following videos.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/SJcAjN-HL_I\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Linear+Growth+Part+1.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cLinear Growth Part 1\u201d here (opens in new window).<\/a><\/p>\n<p><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/4Two_oduhrA\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Linear+Growth+Part+2.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cLinear Growth Part 2\u201d here (opens in new window).<\/a><\/p>\n<p><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/pZ4u3j8Vmzo\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Linear+Growth+Part+3.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cLinear Growth Part 3\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Linear Growth<\/h2>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea<\/strong><\/p>\n<h4><strong>linear growth<\/strong><\/h4>\n<p>If a quantity starts at size [latex]P_0[\/latex]\u00a0and grows by [latex]d[\/latex] every time period, then the quantity after [latex]n[\/latex] time periods can be determined using either of these relations:<\/p>\n<p><strong>Recursive form<\/strong><\/p>\n<p style=\"text-align: center;\">[latex]P_n = P_{n-1} + d[\/latex]<\/p>\n<p><strong>Explicit form<\/strong><\/p>\n<p style=\"text-align: center;\">[latex]P_n = P_0 + d n[\/latex]<\/p>\n<p>In this equation, [latex]d[\/latex]\u00a0represents the <strong>common difference<\/strong> \u2013 the amount that the population changes each time [latex]n[\/latex] increases by [latex]1[\/latex].<\/p>\n<\/div>\n<section class=\"textbox example\">The cost, in dollars, of a gym membership for [latex]n[\/latex] months can be described by the explicit equation [latex]P_n = 70 + 30_n[\/latex]. What does this equation tell us?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q438458\">Show Solution<\/button><\/p>\n<div id=\"q438458\" class=\"hidden-answer\" style=\"display: none\">The value for [latex]P_0[\/latex] in this equation is [latex]70[\/latex], so the initial starting cost is [latex]$70[\/latex]. This tells us that there must be an initiation or start-up fee of [latex]$70[\/latex] to join the gym.<\/p>\n<p>The value for [latex]d[\/latex] in the equation is [latex]30[\/latex], so the cost increases by [latex]$30[\/latex] each month. This tells us that the monthly membership fee for the gym is [latex]$30[\/latex] a month.<\/p>\n<p>The explanation for this example is detailed below.<\/p>\n<p><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/0Uwz5dmLTtk?si=5UwcgQes_viYWnZ7\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Interpreting+a+linear+model.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cInterpreting a linear model\u201d here (opens in new window).<\/a><\/p>\n<\/div>\n<\/div>\n<\/section>\n<h2>Exponential (Population) Growth<\/h2>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea<\/strong><\/p>\n<h4>exponential growth<\/h4>\n<p>If a quantity starts at size [latex]P_0[\/latex] and grows by [latex]R\\%[\/latex] (written as a decimal, [latex]r[\/latex]) every time period, then the quantity after [latex]n[\/latex] time periods can be determined using either of these relations:<\/p>\n<p><strong>Recursive form<\/strong><\/p>\n<p style=\"text-align: center;\">[latex]P_n = (1+r)P_{n-1}[\/latex]<\/p>\n<p><strong>Explicit form<\/strong><\/p>\n<p style=\"text-align: center;\">[latex]P_n = (1+r)^{n}P_0[\/latex]\u00a0 \u00a0 \u00a0 \u00a0 \u00a0or equivalently, [latex]P_n= P_0(1+r)^{n}[\/latex]<\/p>\n<p>We call\u00a0[latex]r[\/latex] the <strong>growth rate<\/strong>.<\/p>\n<p>The term\u00a0[latex](1+r)[\/latex] is called the <strong>growth multiplier<\/strong>, or common ratio.<\/p>\n<\/div>\n<section class=\"textbox example\">Between 2007 and 2008, Olympia, WA grew almost [latex]3\\%[\/latex] to a population of [latex]245[\/latex] thousand people. If this growth rate was to continue, what would the population of Olympia be in 2014?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q54756\">Show Solution<\/button><\/p>\n<div id=\"q54756\" class=\"hidden-answer\" style=\"display: none\">As we did before, we first need to define what year will correspond to [latex]n = 0[\/latex]. Since we know the population in 2008, it would make sense to have 2008 correspond to [latex]n = 0[\/latex], so [latex]P_0 = 245,000[\/latex]. The year 2014 would then be [latex]n = 6[\/latex]. We know the growth rate is [latex]3\\%[\/latex], giving [latex]r = 0.03[\/latex]. Using the explicit form:<\/p>\n<p style=\"text-align: center;\">[latex]P_6 = (1+0.03)^{6}(245,000) = 1.19405(245,000) = 292,542.25[\/latex]<\/p>\n<p>The model predicts that in 2014, Olympia would have a population of about [latex]293[\/latex] thousand people.<\/p>\n<p>The following video explains this example in detail.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Predicting future population using an exponential model\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/CDI4xS65rxY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Predicting+future+population+using+an+exponential+model.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cPredicting future population using an exponential model\u201d here (opens in new window).<\/a><\/p>\n<\/div>\n<\/div>\n<\/section>\n<p>Watch the following videos for more on linear vs. exponential growth.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/_vlXdx-CqM0\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Examples+of+linear+and+exponential+relationships.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cExamples of linear and exponential relationships\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/8OHEgD6YMBw\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Understanding+linear+and+exponential+models+_+Functions+and+their+graphs+_+Algebra+II+_+Khan+Academy.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cUnderstanding linear and exponential models | Functions and their graphs | Algebra II | Khan Academy\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/721RrH6auoU\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Linear+vs.+exponential+growth_+from+data+_+High+School+Math+_+Khan+Academy.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cLinear vs. exponential growth: from data | High School Math | Khan Academy\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":87,"module-header":"fresh_take","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\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/1965"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":18,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/1965\/revisions"}],"predecessor-version":[{"id":14785,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/1965\/revisions\/14785"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/87"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/1965\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=1965"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=1965"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=1965"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=1965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}