{"id":2763,"date":"2024-08-16T00:01:48","date_gmt":"2024-08-16T00:01:48","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=2763"},"modified":"2024-12-02T19:11:13","modified_gmt":"2024-12-02T19:11:13","slug":"series-and-their-notations-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/series-and-their-notations-apply-it-1\/","title":{"raw":"Series and Their Notations: Apply It 1","rendered":"Series and Their Notations: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Use summation notation to write a sum for a series<\/li>\r\n \t<li>Use the formula for the sum of the first [latex]n[\/latex] terms of an arithmetic series<\/li>\r\n \t<li>Use the formula for the sum of the first [latex]n[\/latex] terms of a geometric series<\/li>\r\n \t<li>Use the formula to accurately find the sum of an infinite geometric series<\/li>\r\n \t<li>Solve annuity problems by applying concepts of regular series additions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Solving Application Problems with Arithmetic Series<\/h2>\r\n<section class=\"textbox example\" aria-label=\"Example\">On the Sunday after a minor surgery, a woman is able to walk a half-mile. Each Sunday, she walks an additional quarter-mile. After [latex]8[\/latex] weeks, what will be the total number of miles she has walked?[reveal-answer q=\"455757\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"455757\"]This problem can be modeled by an arithmetic series with [latex]{a}_{1}=\\frac{1}{2}[\/latex] and [latex]d=\\frac{1}{4}[\/latex]. We are looking for the total number of miles walked after [latex]8[\/latex] weeks, so we know that [latex]n=8[\/latex], and we are looking for [latex]{S}_{8}[\/latex]. To find [latex]{a}_{8}[\/latex], we can use the explicit formula for an arithmetic sequence.\r\n<p style=\"text-align: center;\">[latex]\\begin{align} {a}_{n}&amp;={a}_{1}+d\\left(n - 1\\right) \\\\ {a}_{8}&amp;=\\dfrac{1}{2}+\\dfrac{1}{4}\\left(8 - 1\\right)=\\dfrac{9}{4} \\end{align}[\/latex]<\/p>\r\nWe can now use the formula for arithmetic series.\r\n<p style=\"text-align: center;\">[latex]\\begin{align} {S}_{n}&amp;=\\dfrac{n\\left({a}_{1}+{a}_{n}\\right)}{2} \\\\ {S}_{8}&amp;=\\dfrac{8\\left(\\frac{1}{2}+\\frac{9}{4}\\right)}{2}=11 \\end{align}[\/latex]<\/p>\r\nShe will have walked a total of [latex]11[\/latex] miles.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">A parent starts saving for their child's college education when the child is [latex]5[\/latex] years old. They initially deposit [latex]$1000[\/latex] and plan to increase their deposit by [latex]$200[\/latex] each year. If they continue this plan until the child is [latex]18[\/latex] ([latex]14 [\/latex]deposits in total), how much money will they have saved?[reveal-answer q=\"212521\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"212521\"]\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Identify the arithmetic series:\r\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">First term: [latex]a_1 = 1000[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Common difference: [latex]d = 200[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Number of terms: [latex]n = 14[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Find the last term: [latex]a_n = a_1 + (n-1)d = 1000 + (14-1)200 = 3600[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Use the formula for the sum of an arithmetic series: [latex]S_n = \\frac{n}{2}(a_1 + a_n)[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Substitute the values:<center>[latex] \\begin{array}{rcl} S_{14} &amp;=&amp; \\frac{14}{2}(1000 + 3600) \\\\&amp;=&amp; 7 \\cdot 4600 \\\\ &amp;=&amp; 32,200 \\end{array} [\/latex]<\/center><\/li>\r\n<\/ol>\r\n<p class=\"whitespace-pre-wrap break-words\">Therefore, the parent will have saved [latex]$32,200 [\/latex]for their child's college education.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">A new stadium is being built with [latex]30[\/latex] rows of seats. The first row closest to the field has [latex]100[\/latex] seats, and each row behind it has [latex]5[\/latex] more seats than the row in front of it. How many total seats are in the stadium?[reveal-answer q=\"451047\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"451047\"]\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Identify the arithmetic series:\r\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">First term: [latex]a_1 = 100[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Common difference: [latex]d = 5[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Number of terms: [latex]n = 30[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Find the last term: [latex]a_n = a_1 + (n-1)d = 100 + (30-1)5 = 245[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Use the formula for the sum of an arithmetic series: [latex]S_n = \\frac{n}{2}(a_1 + a_n)[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Substitute the values:\r\n<center>[latex] \\begin{array}{rcl} S_{30} &amp;=&amp; \\frac{30}{2}(100 + 245) \\\\ &amp;=&amp; 15 \\cdot 345 \\\\ &amp;=&amp; 5,175 \\end{array} [\/latex]<\/center><\/li>\r\n<\/ol>\r\n<p class=\"whitespace-pre-wrap break-words\">Therefore, there are [latex]5,175[\/latex] seats in total in the stadium.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]24956[\/ohm2_question]<\/section>\r\n<h2>Solving an Application Problem with a Geometric Series<\/h2>\r\n<section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-pre-wrap break-words\">A social media influencer starts a viral marketing campaign for a new product. On the first day, they share the product with [latex]5,000[\/latex] followers. Each day after, only [latex]30 \\%[\/latex] of the people who saw it the previous day share it with new people. How many total people will have seen the product advertisement after [latex]10[\/latex] days?<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">[reveal-answer q=\"43362\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"43362\"]<\/p>\r\n\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Identify the geometric series:\r\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Initial term: [latex]a = 5000[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Common ratio: [latex]r = 0.30[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Number of terms: [latex]n = 10[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Use the formula for the sum of a geometric series: [latex]{S}_{n}=\\dfrac{{a}_{1}\\left(1-{r}^{n}\\right)}{1-r}[\/latex], where [latex]S_n[\/latex] is the sum of the series<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Substitute the values:\r\n<center>[latex] \\begin{array}{rcl} S_{10} &amp;=&amp;\u00a0 \\dfrac{5000(1-(0.30)^{10})}{1-0.30} \\\\\u00a0 &amp;\\approx&amp; 7,142 \\end{array} [\/latex]<\/center><\/li>\r\n<\/ol>\r\n<p class=\"whitespace-pre-wrap break-words\">Therefore, approximately [latex]7,142[\/latex] people will have seen the product advertisement after [latex]10[\/latex] days.<\/p>\r\n<p class=\"whitespace-pre-wrap break-words\">[\/hidden-answer]<\/p>\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">A sample of radioactive material initially weighs [latex]100[\/latex] grams. Each year, [latex]15 \\%[\/latex] of the remaining material decays. What will be the total amount of material that has decayed after [latex]20[\/latex] years?[reveal-answer q=\"316963\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"316963\"]\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Identify the geometric series:\r\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Initial term (amount decaying in first year): [latex]a = 100 \\cdot 0.15 = 15[\/latex] grams<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Common ratio (rate of decay each subsequent year): [latex]r = 0.85[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Number of terms: [latex]n = 20[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Use the formula for the sum of a geometric series: [latex]{S}_{n}=\\dfrac{{a}_{1}\\left(1-{r}^{n}\\right)}{1-r}[\/latex]<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Substitute the values:<center>[latex] \\begin{array}{rcl} S_{20} &amp;=&amp; \\frac{15(1-(0.85)^{20})}{1-0.85} \\\\\u00a0 &amp;\\approx&amp; 96.12 \\end{array} [\/latex]<\/center><\/li>\r\n<\/ol>\r\n<p class=\"whitespace-pre-wrap break-words\">Therefore, approximately [latex]96.12[\/latex] grams of the radioactive material will have decayed after [latex]20[\/latex] years.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]24957[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Use summation notation to write a sum for a series<\/li>\n<li>Use the formula for the sum of the first [latex]n[\/latex] terms of an arithmetic series<\/li>\n<li>Use the formula for the sum of the first [latex]n[\/latex] terms of a geometric series<\/li>\n<li>Use the formula to accurately find the sum of an infinite geometric series<\/li>\n<li>Solve annuity problems by applying concepts of regular series additions<\/li>\n<\/ul>\n<\/section>\n<h2>Solving Application Problems with Arithmetic Series<\/h2>\n<section class=\"textbox example\" aria-label=\"Example\">On the Sunday after a minor surgery, a woman is able to walk a half-mile. Each Sunday, she walks an additional quarter-mile. After [latex]8[\/latex] weeks, what will be the total number of miles she has walked?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q455757\">Show Solution<\/button><\/p>\n<div id=\"q455757\" class=\"hidden-answer\" style=\"display: none\">This problem can be modeled by an arithmetic series with [latex]{a}_{1}=\\frac{1}{2}[\/latex] and [latex]d=\\frac{1}{4}[\/latex]. We are looking for the total number of miles walked after [latex]8[\/latex] weeks, so we know that [latex]n=8[\/latex], and we are looking for [latex]{S}_{8}[\/latex]. To find [latex]{a}_{8}[\/latex], we can use the explicit formula for an arithmetic sequence.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{align} {a}_{n}&={a}_{1}+d\\left(n - 1\\right) \\\\ {a}_{8}&=\\dfrac{1}{2}+\\dfrac{1}{4}\\left(8 - 1\\right)=\\dfrac{9}{4} \\end{align}[\/latex]<\/p>\n<p>We can now use the formula for arithmetic series.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{align} {S}_{n}&=\\dfrac{n\\left({a}_{1}+{a}_{n}\\right)}{2} \\\\ {S}_{8}&=\\dfrac{8\\left(\\frac{1}{2}+\\frac{9}{4}\\right)}{2}=11 \\end{align}[\/latex]<\/p>\n<p>She will have walked a total of [latex]11[\/latex] miles.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">A parent starts saving for their child&#8217;s college education when the child is [latex]5[\/latex] years old. They initially deposit [latex]$1000[\/latex] and plan to increase their deposit by [latex]$200[\/latex] each year. If they continue this plan until the child is [latex]18[\/latex] ([latex]14[\/latex]deposits in total), how much money will they have saved?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q212521\">Show Answer<\/button><\/p>\n<div id=\"q212521\" class=\"hidden-answer\" style=\"display: none\">\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Identify the arithmetic series:\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">First term: [latex]a_1 = 1000[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Common difference: [latex]d = 200[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Number of terms: [latex]n = 14[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li class=\"whitespace-normal break-words\">Find the last term: [latex]a_n = a_1 + (n-1)d = 1000 + (14-1)200 = 3600[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Use the formula for the sum of an arithmetic series: [latex]S_n = \\frac{n}{2}(a_1 + a_n)[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Substitute the values:\n<div style=\"text-align: center;\">[latex]\\begin{array}{rcl} S_{14} &=& \\frac{14}{2}(1000 + 3600) \\\\&=& 7 \\cdot 4600 \\\\ &=& 32,200 \\end{array}[\/latex]<\/div>\n<\/li>\n<\/ol>\n<p class=\"whitespace-pre-wrap break-words\">Therefore, the parent will have saved [latex]$32,200[\/latex]for their child&#8217;s college education.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">A new stadium is being built with [latex]30[\/latex] rows of seats. The first row closest to the field has [latex]100[\/latex] seats, and each row behind it has [latex]5[\/latex] more seats than the row in front of it. How many total seats are in the stadium?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q451047\">Show Answer<\/button><\/p>\n<div id=\"q451047\" class=\"hidden-answer\" style=\"display: none\">\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Identify the arithmetic series:\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">First term: [latex]a_1 = 100[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Common difference: [latex]d = 5[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Number of terms: [latex]n = 30[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li class=\"whitespace-normal break-words\">Find the last term: [latex]a_n = a_1 + (n-1)d = 100 + (30-1)5 = 245[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Use the formula for the sum of an arithmetic series: [latex]S_n = \\frac{n}{2}(a_1 + a_n)[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Substitute the values:\n<div style=\"text-align: center;\">[latex]\\begin{array}{rcl} S_{30} &=& \\frac{30}{2}(100 + 245) \\\\ &=& 15 \\cdot 345 \\\\ &=& 5,175 \\end{array}[\/latex]<\/div>\n<\/li>\n<\/ol>\n<p class=\"whitespace-pre-wrap break-words\">Therefore, there are [latex]5,175[\/latex] seats in total in the stadium.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm24956\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=24956&theme=lumen&iframe_resize_id=ohm24956&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h2>Solving an Application Problem with a Geometric Series<\/h2>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-pre-wrap break-words\">A social media influencer starts a viral marketing campaign for a new product. On the first day, they share the product with [latex]5,000[\/latex] followers. Each day after, only [latex]30 \\%[\/latex] of the people who saw it the previous day share it with new people. How many total people will have seen the product advertisement after [latex]10[\/latex] days?<\/p>\n<p class=\"whitespace-pre-wrap break-words\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q43362\">Show Answer<\/button><\/p>\n<div id=\"q43362\" class=\"hidden-answer\" style=\"display: none\">\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Identify the geometric series:\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Initial term: [latex]a = 5000[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Common ratio: [latex]r = 0.30[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Number of terms: [latex]n = 10[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li class=\"whitespace-normal break-words\">Use the formula for the sum of a geometric series: [latex]{S}_{n}=\\dfrac{{a}_{1}\\left(1-{r}^{n}\\right)}{1-r}[\/latex], where [latex]S_n[\/latex] is the sum of the series<\/li>\n<li class=\"whitespace-normal break-words\">Substitute the values:\n<div style=\"text-align: center;\">[latex]\\begin{array}{rcl} S_{10} &=&\u00a0 \\dfrac{5000(1-(0.30)^{10})}{1-0.30} \\\\\u00a0 &\\approx& 7,142 \\end{array}[\/latex]<\/div>\n<\/li>\n<\/ol>\n<p class=\"whitespace-pre-wrap break-words\">Therefore, approximately [latex]7,142[\/latex] people will have seen the product advertisement after [latex]10[\/latex] days.<\/p>\n<p class=\"whitespace-pre-wrap break-words\"><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">A sample of radioactive material initially weighs [latex]100[\/latex] grams. Each year, [latex]15 \\%[\/latex] of the remaining material decays. What will be the total amount of material that has decayed after [latex]20[\/latex] years?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q316963\">Show Answer<\/button><\/p>\n<div id=\"q316963\" class=\"hidden-answer\" style=\"display: none\">\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Identify the geometric series:\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Initial term (amount decaying in first year): [latex]a = 100 \\cdot 0.15 = 15[\/latex] grams<\/li>\n<li class=\"whitespace-normal break-words\">Common ratio (rate of decay each subsequent year): [latex]r = 0.85[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Number of terms: [latex]n = 20[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li class=\"whitespace-normal break-words\">Use the formula for the sum of a geometric series: [latex]{S}_{n}=\\dfrac{{a}_{1}\\left(1-{r}^{n}\\right)}{1-r}[\/latex]<\/li>\n<li class=\"whitespace-normal break-words\">Substitute the values:\n<div style=\"text-align: center;\">[latex]\\begin{array}{rcl} S_{20} &=& \\frac{15(1-(0.85)^{20})}{1-0.85} \\\\\u00a0 &\\approx& 96.12 \\end{array}[\/latex]<\/div>\n<\/li>\n<\/ol>\n<p class=\"whitespace-pre-wrap break-words\">Therefore, approximately [latex]96.12[\/latex] grams of the radioactive material will have decayed after [latex]20[\/latex] years.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm24957\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=24957&theme=lumen&iframe_resize_id=ohm24957&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":27,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":363,"module-header":"apply_it","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\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/2763"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":14,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/2763\/revisions"}],"predecessor-version":[{"id":6537,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/2763\/revisions\/6537"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/363"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/2763\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=2763"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=2763"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=2763"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=2763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}