{"id":3156,"date":"2025-08-15T22:21:59","date_gmt":"2025-08-15T22:21:59","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=3156"},"modified":"2026-03-16T20:58:23","modified_gmt":"2026-03-16T20:58:23","slug":"graphs-of-exponential-functions-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/graphs-of-exponential-functions-apply-it\/","title":{"raw":"Graphs of Exponential Functions: Apply It","rendered":"Graphs of Exponential Functions: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Graph exponential functions.<\/li>\r\n \t<li>Graph exponential functions using transformations.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<div>\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Bacterial Growth in Food Safety<\/h2>\r\n<p class=\"whitespace-normal break-words\">Dr. Martinez works as a food safety inspector for a restaurant chain. She needs to understand how bacteria multiply in food left at room temperature to determine safe storage times and create effective food safety protocols.<\/p>\r\n<p class=\"whitespace-normal break-words\">When food is left at room temperature (70\u00b0F), certain harmful bacteria can double every 20 minutes. Starting with an initial population of 100 bacteria, Dr. Martinez needs to graph this growth pattern, modeled by [latex]f(t)=100(2)^{\\frac{t}{20}}[\/latex] where [latex]t[\/latex] represents the time in minutes, and use it to make critical food safety decisions.<\/p>\r\n\r\n<section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-normal break-words\">Graph the bacterial growth modeled by [latex]f(t)=100(2)^{\\frac{t}{20}}[\/latex].<\/p>\r\n[reveal-answer q=\"835097\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"835097\"]\r\n\r\nStart by creating a table of values. Since we know the bacteria double every [latex]20[\/latex] minutes we'll count the inputs by [latex]20[\/latex]\r\n<table style=\"width: 90.1274%; height: 122px;\"><caption>P(t) = 100 \u00b7 2^(t\/20)<\/caption>\r\n<thead>\r\n<tr style=\"height: 22px;\">\r\n<th style=\"width: 9.91379%; height: 22px;\" scope=\"col\">t<\/th>\r\n<th style=\"width: 72.8448%; height: 22px;\" scope=\"col\">Calculation<\/th>\r\n<th style=\"width: 87.931%; height: 22px;\" scope=\"col\">P(t)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 25px;\">\r\n<td style=\"width: 9.91379%; text-align: center; height: 25px;\">0<\/td>\r\n<td style=\"width: 72.8448%; text-align: center; height: 25px;\">100 \u00d7 2<sup>0\/20<\/sup> = 100 \u00d7 2<sup>0<\/sup><\/td>\r\n<td style=\"width: 87.931%; text-align: center; height: 25px;\">100<\/td>\r\n<\/tr>\r\n<tr style=\"height: 25px;\">\r\n<td style=\"width: 9.91379%; text-align: center; height: 25px;\">20<\/td>\r\n<td style=\"width: 72.8448%; text-align: center; height: 25px;\">100 \u00d7 2<sup>20\/20<\/sup> = 100 \u00d7 2<sup>1<\/sup><\/td>\r\n<td style=\"width: 87.931%; text-align: center; height: 25px;\">200<\/td>\r\n<\/tr>\r\n<tr style=\"height: 25px;\">\r\n<td style=\"width: 9.91379%; text-align: center; height: 25px;\">40<\/td>\r\n<td style=\"width: 72.8448%; text-align: center; height: 25px;\">100 \u00d7 2<sup>40\/20<\/sup> = 100 \u00d7 2<sup>2<\/sup><\/td>\r\n<td style=\"width: 87.931%; text-align: center; height: 25px;\">400<\/td>\r\n<\/tr>\r\n<tr style=\"height: 25px;\">\r\n<td style=\"width: 9.91379%; text-align: center; height: 25px;\">60<\/td>\r\n<td style=\"width: 72.8448%; text-align: center; height: 25px;\">100 \u00d7 2<sup>60\/20<\/sup> = 100 \u00d7 2<sup>3<\/sup><\/td>\r\n<td style=\"width: 87.931%; text-align: center; height: 25px;\">800<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNow we plot the points:\r\n\r\n<img class=\"alignnone  wp-image-3812\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2.png\" alt=\"\" width=\"516\" height=\"516\" \/>\r\n\r\n[\/hidden-answer]\r\n<p class=\"whitespace-normal break-words\"><\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]311266[\/ohm_question]<\/section><section aria-label=\"Try It\"><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]311267[\/ohm_question]<\/section><\/section><section class=\"textbox connectIt\" aria-label=\"Connect It\">You can learn more about food safety guidelines and proper food temperatures at http:\/\/www.fsis.usda.gov\/food-safety\/safe-food-handling-and-preparation\/food-safety-basics\/steps-keep-food-safe.<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-normal break-words\">Dr. Martinez finds that some foods start with higher baseline contamination. Deli meats might begin with 500 bacteria instead of 100.<\/p>\r\n<p class=\"whitespace-normal break-words\">The new model becomes: [latex]P_2(t) = 500 \\cdot 2^{\\frac{t}{20}}[\/latex].<\/p>\r\nGraph the new model and compare it to the original.\r\n\r\n[reveal-answer q=\"877680\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"877680\"]The two graphs are shown below:\r\n\r\n<img class=\"alignnone size-full wp-image-3813\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4.png\" alt=\"\" width=\"800\" height=\"800\" \/>\r\n\r\nAlthough it's often easier to compare from the table of values:\r\n<table style=\"width: 95.2347%;\"><caption>Comparison of P\u2081(t) = 100\u00b72^(t\/20) and P\u2082(t) = 500\u00b72^(t\/20)<\/caption>\r\n<thead>\r\n<tr>\r\n<th style=\"width: 19.7368%;\" scope=\"col\">t<\/th>\r\n<th style=\"width: 34.2105%;\" scope=\"col\">P\u2081(t)<\/th>\r\n<th style=\"width: 220.395%;\" scope=\"col\">P\u2082(t)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">0<\/td>\r\n<td style=\"width: 34.2105%;\">100<\/td>\r\n<td style=\"width: 220.395%;\">500<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">20<\/td>\r\n<td style=\"width: 34.2105%;\">200<\/td>\r\n<td style=\"width: 220.395%;\">1000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">40<\/td>\r\n<td style=\"width: 34.2105%;\">400<\/td>\r\n<td style=\"width: 220.395%;\">2000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">60<\/td>\r\n<td style=\"width: 34.2105%;\">800<\/td>\r\n<td style=\"width: 220.395%;\">4000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">80<\/td>\r\n<td style=\"width: 34.2105%;\">1600<\/td>\r\n<td style=\"width: 220.395%;\">8000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">100<\/td>\r\n<td style=\"width: 34.2105%;\">3200<\/td>\r\n<td style=\"width: 220.395%;\">16000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">120<\/td>\r\n<td style=\"width: 34.2105%;\">6400<\/td>\r\n<td style=\"width: 220.395%;\">32000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">140<\/td>\r\n<td style=\"width: 34.2105%;\">12800<\/td>\r\n<td style=\"width: 220.395%;\">64000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">160<\/td>\r\n<td style=\"width: 34.2105%;\">25600<\/td>\r\n<td style=\"width: 220.395%;\">128000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 19.7368%;\">180<\/td>\r\n<td style=\"width: 34.2105%;\">51200<\/td>\r\n<td style=\"width: 220.395%;\">256000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nFrom the graph and table we can see that if the bacteria starts with [latex]500[\/latex] instead of [latex]100[\/latex], it will reach the [latex]10,000[\/latex] safety threshold [latex]40[\/latex] minutes earlier.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section><\/div>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Graph exponential functions.<\/li>\n<li>Graph exponential functions using transformations.<\/li>\n<\/ul>\n<\/section>\n<div>\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Bacterial Growth in Food Safety<\/h2>\n<p class=\"whitespace-normal break-words\">Dr. Martinez works as a food safety inspector for a restaurant chain. She needs to understand how bacteria multiply in food left at room temperature to determine safe storage times and create effective food safety protocols.<\/p>\n<p class=\"whitespace-normal break-words\">When food is left at room temperature (70\u00b0F), certain harmful bacteria can double every 20 minutes. Starting with an initial population of 100 bacteria, Dr. Martinez needs to graph this growth pattern, modeled by [latex]f(t)=100(2)^{\\frac{t}{20}}[\/latex] where [latex]t[\/latex] represents the time in minutes, and use it to make critical food safety decisions.<\/p>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-normal break-words\">Graph the bacterial growth modeled by [latex]f(t)=100(2)^{\\frac{t}{20}}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q835097\">Show Solution<\/button><\/p>\n<div id=\"q835097\" class=\"hidden-answer\" style=\"display: none\">\n<p>Start by creating a table of values. Since we know the bacteria double every [latex]20[\/latex] minutes we&#8217;ll count the inputs by [latex]20[\/latex]<\/p>\n<table style=\"width: 90.1274%; height: 122px;\">\n<caption>P(t) = 100 \u00b7 2^(t\/20)<\/caption>\n<thead>\n<tr style=\"height: 22px;\">\n<th style=\"width: 9.91379%; height: 22px;\" scope=\"col\">t<\/th>\n<th style=\"width: 72.8448%; height: 22px;\" scope=\"col\">Calculation<\/th>\n<th style=\"width: 87.931%; height: 22px;\" scope=\"col\">P(t)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 25px;\">\n<td style=\"width: 9.91379%; text-align: center; height: 25px;\">0<\/td>\n<td style=\"width: 72.8448%; text-align: center; height: 25px;\">100 \u00d7 2<sup>0\/20<\/sup> = 100 \u00d7 2<sup>0<\/sup><\/td>\n<td style=\"width: 87.931%; text-align: center; height: 25px;\">100<\/td>\n<\/tr>\n<tr style=\"height: 25px;\">\n<td style=\"width: 9.91379%; text-align: center; height: 25px;\">20<\/td>\n<td style=\"width: 72.8448%; text-align: center; height: 25px;\">100 \u00d7 2<sup>20\/20<\/sup> = 100 \u00d7 2<sup>1<\/sup><\/td>\n<td style=\"width: 87.931%; text-align: center; height: 25px;\">200<\/td>\n<\/tr>\n<tr style=\"height: 25px;\">\n<td style=\"width: 9.91379%; text-align: center; height: 25px;\">40<\/td>\n<td style=\"width: 72.8448%; text-align: center; height: 25px;\">100 \u00d7 2<sup>40\/20<\/sup> = 100 \u00d7 2<sup>2<\/sup><\/td>\n<td style=\"width: 87.931%; text-align: center; height: 25px;\">400<\/td>\n<\/tr>\n<tr style=\"height: 25px;\">\n<td style=\"width: 9.91379%; text-align: center; height: 25px;\">60<\/td>\n<td style=\"width: 72.8448%; text-align: center; height: 25px;\">100 \u00d7 2<sup>60\/20<\/sup> = 100 \u00d7 2<sup>3<\/sup><\/td>\n<td style=\"width: 87.931%; text-align: center; height: 25px;\">800<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Now we plot the points:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone  wp-image-3812\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2.png\" alt=\"\" width=\"516\" height=\"516\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2.png 800w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2-300x300.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2-150x150.png 150w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2-768x768.png 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2-65x65.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2-225x225.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09163531\/desmos-graph-2-350x350.png 350w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<\/div>\n<\/div>\n<p class=\"whitespace-normal break-words\">\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm311266\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=311266&theme=lumen&iframe_resize_id=ohm311266&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section aria-label=\"Try It\">\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm311267\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=311267&theme=lumen&iframe_resize_id=ohm311267&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n<section class=\"textbox connectIt\" aria-label=\"Connect It\">You can learn more about food safety guidelines and proper food temperatures at http:\/\/www.fsis.usda.gov\/food-safety\/safe-food-handling-and-preparation\/food-safety-basics\/steps-keep-food-safe.<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-normal break-words\">Dr. Martinez finds that some foods start with higher baseline contamination. Deli meats might begin with 500 bacteria instead of 100.<\/p>\n<p class=\"whitespace-normal break-words\">The new model becomes: [latex]P_2(t) = 500 \\cdot 2^{\\frac{t}{20}}[\/latex].<\/p>\n<p>Graph the new model and compare it to the original.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q877680\">Show Solution<\/button><\/p>\n<div id=\"q877680\" class=\"hidden-answer\" style=\"display: none\">The two graphs are shown below:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3813\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4.png\" alt=\"\" width=\"800\" height=\"800\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4.png 800w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4-300x300.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4-150x150.png 150w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4-768x768.png 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4-65x65.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4-225x225.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/61\/2025\/08\/09164749\/desmos-graph-4-350x350.png 350w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>Although it&#8217;s often easier to compare from the table of values:<\/p>\n<table style=\"width: 95.2347%;\">\n<caption>Comparison of P\u2081(t) = 100\u00b72^(t\/20) and P\u2082(t) = 500\u00b72^(t\/20)<\/caption>\n<thead>\n<tr>\n<th style=\"width: 19.7368%;\" scope=\"col\">t<\/th>\n<th style=\"width: 34.2105%;\" scope=\"col\">P\u2081(t)<\/th>\n<th style=\"width: 220.395%;\" scope=\"col\">P\u2082(t)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"width: 19.7368%;\">0<\/td>\n<td style=\"width: 34.2105%;\">100<\/td>\n<td style=\"width: 220.395%;\">500<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">20<\/td>\n<td style=\"width: 34.2105%;\">200<\/td>\n<td style=\"width: 220.395%;\">1000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">40<\/td>\n<td style=\"width: 34.2105%;\">400<\/td>\n<td style=\"width: 220.395%;\">2000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">60<\/td>\n<td style=\"width: 34.2105%;\">800<\/td>\n<td style=\"width: 220.395%;\">4000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">80<\/td>\n<td style=\"width: 34.2105%;\">1600<\/td>\n<td style=\"width: 220.395%;\">8000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">100<\/td>\n<td style=\"width: 34.2105%;\">3200<\/td>\n<td style=\"width: 220.395%;\">16000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">120<\/td>\n<td style=\"width: 34.2105%;\">6400<\/td>\n<td style=\"width: 220.395%;\">32000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">140<\/td>\n<td style=\"width: 34.2105%;\">12800<\/td>\n<td style=\"width: 220.395%;\">64000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">160<\/td>\n<td style=\"width: 34.2105%;\">25600<\/td>\n<td style=\"width: 220.395%;\">128000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.7368%;\">180<\/td>\n<td style=\"width: 34.2105%;\">51200<\/td>\n<td style=\"width: 220.395%;\">256000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>From the graph and table we can see that if the bacteria starts with [latex]500[\/latex] instead of [latex]100[\/latex], it will reach the [latex]10,000[\/latex] safety threshold [latex]40[\/latex] minutes earlier.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n","protected":false},"author":67,"menu_order":10,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":105,"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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3156"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3156\/revisions"}],"predecessor-version":[{"id":5876,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3156\/revisions\/5876"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/105"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3156\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=3156"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=3156"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=3156"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=3156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}