{"id":8440,"date":"2023-09-29T14:59:16","date_gmt":"2023-09-29T14:59:16","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=8440"},"modified":"2025-03-20T14:58:32","modified_gmt":"2025-03-20T14:58:32","slug":"introduction-to-modeling-get-stronger","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/introduction-to-modeling-get-stronger\/","title":{"raw":"Introduction to Modeling: Get Stronger","rendered":"Introduction to Modeling: Get Stronger"},"content":{"raw":"
    \r\n\t
  1. Marko currently has [latex]20[\/latex] tulips in his yard. Each year he plants [latex]5[\/latex] more.
    \r\n
      \r\n\t
    1. Write a recursive formula for the number of tulips Marko has<\/li>\r\n\t
    2. Write an explicit formula for the number of tulips Marko has<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
    3. Pam is a Disc Jockey. Every week she buys [latex]3[\/latex] new albums to keep her collection current. She currently owns [latex]450[\/latex] albums.
      \r\n
        \r\n\t
      1. Write a recursive formula for the number of albums Pam has<\/li>\r\n\t
      2. Write an explicit formula for the number of albums Pam has<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
      3. A store\u2019s sales (in thousands of dollars) grow according to the recursive rule [latex]P_n = P_{n-1} + 15[\/latex] with initial population [latex]P_0 = 40[\/latex].
        \r\n
          \r\n\t
        1. Calculate [latex]P_1[\/latex] and\u00a0[latex]P_2[\/latex].<\/li>\r\n\t
        2. Find an explicit formula for [latex]P_n[\/latex].<\/li>\r\n\t
        3. Use your formula to predict the store\u2019s sales in [latex]10[\/latex] years<\/li>\r\n\t
        4. When will the store\u2019s sales exceed [latex]$100,000[\/latex]?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
        5. The number of houses in a town has been growing according to the recursive rule [latex]P_n = P_{n-1} + 30[\/latex], with initial population [latex]P_0 = 200[\/latex].
          \r\n
            \r\n\t
          1. Calculate [latex]P_1[\/latex] and\u00a0[latex]P_2[\/latex].<\/li>\r\n\t
          2. Find an explicit formula for [latex]P_n[\/latex].<\/li>\r\n\t
          3. Use your formula to predict the number of houses in [latex]10[\/latex] years<\/li>\r\n\t
          4. When will the number of houses reach [latex]400[\/latex] houses?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
          5. A population of beetles is growing according to a linear growth model. The initial population (week 0) was [latex]P_0=3[\/latex], and the population after [latex]8[\/latex] weeks is [latex]P_8=67[\/latex].
            \r\n
              \r\n\t
            1. Find an explicit formula for the beetle population in week [latex]n[\/latex].<\/li>\r\n\t
            2. After how many weeks will the beetle population reach [latex]187[\/latex]?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
            3. The number of streetlights in a town is growing linearly. Four months ago [latex]n = 0[\/latex], there were [latex]130[\/latex] lights. Now [latex]n=4[\/latex], there are [latex]146[\/latex] lights. If this trend continues,
              \r\n
                \r\n\t
              1. Find an explicit formula for the number of lights in month [latex]n[\/latex]<\/li>\r\n\t
              2. How many months will it take to reach [latex]200[\/latex] lights?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
              3. Tacoma's population in 2000 was about [latex]200[\/latex] thousand, and had been growing by about [latex]9\\%[\/latex] each year.
                \r\n
                  \r\n\t
                1. Write a recursive formula for the population of Tacoma<\/li>\r\n\t
                2. Write an explicit formula for the population of Tacoma<\/li>\r\n\t
                3. If this trend continues, what will Tacoma's population be in 2016?<\/li>\r\n\t
                4. When does this model predict Tacoma\u2019s population to exceed [latex]400[\/latex] thousand?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
                5. Portland's population in 2007 was about [latex]568[\/latex] thousand, and had been growing by about [latex]1.1\\%[\/latex] each year.
                  \r\n
                    \r\n\t
                  1. Write a recursive formula for the population of Portland<\/li>\r\n\t
                  2. Write an explicit formula for the population of Portland<\/li>\r\n\t
                  3. If this trend continues, what will Portland's population be in 2016?<\/li>\r\n\t
                  4. If this trend continues, when will Portland\u2019s population reach [latex]700[\/latex] thousand?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
                  5. Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth rate was around [latex]190\\%[\/latex]. In 1983, about [latex]1700[\/latex] people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2005?<\/li>\r\n\t
                  6. The population of the world in 1987 was [latex]5[\/latex] billion and the annual growth rate was estimated at [latex]2[\/latex] percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2015.<\/li>\r\n\t
                  7. A bacteria culture is started with [latex]300[\/latex] bacteria. After [latex]4[\/latex] hours, the population has grown to [latex]500[\/latex] bacteria. If the population grows exponentially,
                    \r\n
                      \r\n\t
                    1. Write a recursive formula for the number of bacteria<\/li>\r\n\t
                    2. Write an explicit formula for the number of bacteria<\/li>\r\n\t
                    3. If this trend continues, how many bacteria will there be in [latex]1[\/latex] day?<\/li>\r\n\t
                    4. How long does it take for the culture to triple in size?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
                    5. A native wolf species has been reintroduced into a national forest. Originally [latex]200[\/latex] wolves were transplanted. After [latex]3[\/latex] years, the population had grown to [latex]270[\/latex] wolves. If the population grows exponentially,
                      \r\n
                        \r\n\t
                      1. Write a recursive formula for the number of wolves<\/li>\r\n\t
                      2. Write an explicit formula for the number of wolves<\/li>\r\n\t
                      3. If this trend continues, how many wolves will there be in [latex]10[\/latex] years?<\/li>\r\n\t
                      4. If this trend continues, how long will it take the population to grow to [latex]1000[\/latex] wolves?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
                      5. In 1968, the U.S. minimum wage was [latex]$1.60[\/latex] per hour. In 1976, the minimum wage was [latex]$2.30[\/latex] per hour. Assume the minimum wage grows according to an exponential model where [latex]n[\/latex] represents the time in years after 1960.
                        \r\n
                          \r\n\t
                        1. Find an explicit formula for the minimum wage.<\/li>\r\n\t
                        2. What does the model predict for the minimum wage in 1960?<\/li>\r\n\t
                        3. If the minimum wage was [latex]$5.15[\/latex] in 1996, is this above, below or equal to what the model predicts?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
                        4. The population of a small town can be described by the equation [latex]P_n = 4000+70n[\/latex], where [latex]n[\/latex] is the number of years after 2005. Explain in words what this equation tells us about how the population is changing.<\/li>\r\n\t
                        5. The population of a small town can be described by the equation [latex]P_n = 4000(1.04)n[\/latex], where [latex]n[\/latex] is the number of years after 2005. Explain in words what this equation tells us about how the population is changing.<\/li>\r\n\t
                        6. A new truck costs [latex]$32,000[\/latex]. The car\u2019s value will depreciate over time, which means it will lose value. For tax purposes, depreciation is usually calculated linearly. If the truck is worth [latex]$24,500[\/latex] after three years, write an explicit formula for the value of the car after [latex]n[\/latex] years.<\/li>\r\n\t
                        7. Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying, \"In my day, you could buy a cup of coffee for a nickel\"). Suppose inflation decreases the value of money by [latex]5\\%[\/latex] each year. In other words, if you have [latex]$1[\/latex] this year, next year it will only buy you [latex]$0.95[\/latex] worth of stuff. How much will [latex]$100[\/latex] buy you in [latex]20[\/latex] years?<\/li>\r\n\t
                        8. Suppose that you have a bowl of [latex]500[\/latex] M&M candies, and each day you eat [latex]\\frac{1}{4}[\/latex] of the candies you have. Is the number of candies left changing linearly or exponentially? Write an equation to model the number of candies left after [latex]n[\/latex] days.<\/li>\r\n\t
                        9. A warm object in a cooler room will decrease in temperature exponentially, approaching the room temperature according to the formula where [latex]T_n[\/latex] is the temperature after [latex]n[\/latex] minutes, [latex]r[\/latex] is the rate at which temperature is changing, [latex]a[\/latex] is a constant, and [latex]Tr[\/latex] is the temperature of the room. Forensic investigators can use this to predict the time of death of a homicide victim. Suppose that when a body was discovered [latex](n=0)[\/latex] it was [latex]85[\/latex] degrees. After [latex]20[\/latex] minutes, the temperature was measured again to be [latex]80[\/latex] degrees. The body was in a [latex]70[\/latex] degree room.
                          \r\n
                            \r\n\t
                          1. Use the given information with the formula provided to find a formula for the temperature of the body.<\/li>\r\n\t
                          2. When did the victim die, if the body started at [latex]98.6[\/latex] degrees?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
                          3. Recursive equations can be very handy for modeling complicated situations for which explicit equations would be hard to interpret. As an example, consider a lake in which 2000 fish currently reside. The fish population grows by [latex]10\\%[\/latex] each year, but every year [latex]100[\/latex] fish are harvested from the lake by people fishing.
                            \r\n
                              \r\n\t
                            1. Write a recursive equation for the number of fish in the lake after [latex]n[\/latex] years.<\/li>\r\n\t
                            2. Calculate the population after [latex]1[\/latex] and [latex]2[\/latex] years. Does the population appear to be increasing or decreasing?<\/li>\r\n\t
                            3. What is the maximum number of fish that could be harvested each year without causing the fish population to decrease in the long run?<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t
                            4. The number of Starbucks stores grew after first opened. The number of stores from 1990-2007, as reported on their corporate website[footnote]https:\/\/stories.starbucks.com\/uploads\/2019\/01\/AboutUs-Company-Timeline-1.6.21-FINAL.pdf[\/footnote], is shown below.
                              \r\n
                                \r\n\t
                              1. Carefully plot the data. Does is appear to be changing linearly or exponentially?<\/li>\r\n\t
                              2. Try finding an equation to model the data by picking two points to work from. How well does the equation model the data?<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

                                \"clipboard_e723972894bc819360fb5aa9fe3e212fd.png\"<\/p>\r\n

                                  \r\n\t
                                1. Thomas Malthus was an economist who put forth the principle that population grows based on an exponential growth model, while food and resources grow based on a linear growth model. Based on this, Malthus predicted that eventually demand for food and resources would out outgrow supply, with doom-and-gloom consequences. Do some research about Malthus to answer these questions.
                                  \r\n
                                    \r\n\t
                                  1. What societal changes did Malthus propose to avoid the doom-and-gloom outcome he was predicting?<\/li>\r\n\t
                                  2. Why do you think his predictions did not occur?<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"
                                      \n
                                    1. Marko currently has [latex]20[\/latex] tulips in his yard. Each year he plants [latex]5[\/latex] more.\n
                                        \n
                                      1. Write a recursive formula for the number of tulips Marko has<\/li>\n
                                      2. Write an explicit formula for the number of tulips Marko has<\/li>\n<\/ol>\n<\/li>\n
                                      3. Pam is a Disc Jockey. Every week she buys [latex]3[\/latex] new albums to keep her collection current. She currently owns [latex]450[\/latex] albums.\n
                                          \n
                                        1. Write a recursive formula for the number of albums Pam has<\/li>\n
                                        2. Write an explicit formula for the number of albums Pam has<\/li>\n<\/ol>\n<\/li>\n
                                        3. A store\u2019s sales (in thousands of dollars) grow according to the recursive rule [latex]P_n = P_{n-1} + 15[\/latex] with initial population [latex]P_0 = 40[\/latex].\n
                                            \n
                                          1. Calculate [latex]P_1[\/latex] and\u00a0[latex]P_2[\/latex].<\/li>\n
                                          2. Find an explicit formula for [latex]P_n[\/latex].<\/li>\n
                                          3. Use your formula to predict the store\u2019s sales in [latex]10[\/latex] years<\/li>\n
                                          4. When will the store\u2019s sales exceed [latex]$100,000[\/latex]?<\/li>\n<\/ol>\n<\/li>\n
                                          5. The number of houses in a town has been growing according to the recursive rule [latex]P_n = P_{n-1} + 30[\/latex], with initial population [latex]P_0 = 200[\/latex].\n
                                              \n
                                            1. Calculate [latex]P_1[\/latex] and\u00a0[latex]P_2[\/latex].<\/li>\n
                                            2. Find an explicit formula for [latex]P_n[\/latex].<\/li>\n
                                            3. Use your formula to predict the number of houses in [latex]10[\/latex] years<\/li>\n
                                            4. When will the number of houses reach [latex]400[\/latex] houses?<\/li>\n<\/ol>\n<\/li>\n
                                            5. A population of beetles is growing according to a linear growth model. The initial population (week 0) was [latex]P_0=3[\/latex], and the population after [latex]8[\/latex] weeks is [latex]P_8=67[\/latex].\n
                                                \n
                                              1. Find an explicit formula for the beetle population in week [latex]n[\/latex].<\/li>\n
                                              2. After how many weeks will the beetle population reach [latex]187[\/latex]?<\/li>\n<\/ol>\n<\/li>\n
                                              3. The number of streetlights in a town is growing linearly. Four months ago [latex]n = 0[\/latex], there were [latex]130[\/latex] lights. Now [latex]n=4[\/latex], there are [latex]146[\/latex] lights. If this trend continues,\n
                                                  \n
                                                1. Find an explicit formula for the number of lights in month [latex]n[\/latex]<\/li>\n
                                                2. How many months will it take to reach [latex]200[\/latex] lights?<\/li>\n<\/ol>\n<\/li>\n
                                                3. Tacoma’s population in 2000 was about [latex]200[\/latex] thousand, and had been growing by about [latex]9\\%[\/latex] each year.\n
                                                    \n
                                                  1. Write a recursive formula for the population of Tacoma<\/li>\n
                                                  2. Write an explicit formula for the population of Tacoma<\/li>\n
                                                  3. If this trend continues, what will Tacoma’s population be in 2016?<\/li>\n
                                                  4. When does this model predict Tacoma\u2019s population to exceed [latex]400[\/latex] thousand?<\/li>\n<\/ol>\n<\/li>\n
                                                  5. Portland’s population in 2007 was about [latex]568[\/latex] thousand, and had been growing by about [latex]1.1\\%[\/latex] each year.\n
                                                      \n
                                                    1. Write a recursive formula for the population of Portland<\/li>\n
                                                    2. Write an explicit formula for the population of Portland<\/li>\n
                                                    3. If this trend continues, what will Portland’s population be in 2016?<\/li>\n
                                                    4. If this trend continues, when will Portland\u2019s population reach [latex]700[\/latex] thousand?<\/li>\n<\/ol>\n<\/li>\n
                                                    5. Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth rate was around [latex]190\\%[\/latex]. In 1983, about [latex]1700[\/latex] people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2005?<\/li>\n
                                                    6. The population of the world in 1987 was [latex]5[\/latex] billion and the annual growth rate was estimated at [latex]2[\/latex] percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2015.<\/li>\n
                                                    7. A bacteria culture is started with [latex]300[\/latex] bacteria. After [latex]4[\/latex] hours, the population has grown to [latex]500[\/latex] bacteria. If the population grows exponentially,\n
                                                        \n
                                                      1. Write a recursive formula for the number of bacteria<\/li>\n
                                                      2. Write an explicit formula for the number of bacteria<\/li>\n
                                                      3. If this trend continues, how many bacteria will there be in [latex]1[\/latex] day?<\/li>\n
                                                      4. How long does it take for the culture to triple in size?<\/li>\n<\/ol>\n<\/li>\n
                                                      5. A native wolf species has been reintroduced into a national forest. Originally [latex]200[\/latex] wolves were transplanted. After [latex]3[\/latex] years, the population had grown to [latex]270[\/latex] wolves. If the population grows exponentially,\n
                                                          \n
                                                        1. Write a recursive formula for the number of wolves<\/li>\n
                                                        2. Write an explicit formula for the number of wolves<\/li>\n
                                                        3. If this trend continues, how many wolves will there be in [latex]10[\/latex] years?<\/li>\n
                                                        4. If this trend continues, how long will it take the population to grow to [latex]1000[\/latex] wolves?<\/li>\n<\/ol>\n<\/li>\n
                                                        5. In 1968, the U.S. minimum wage was [latex]$1.60[\/latex] per hour. In 1976, the minimum wage was [latex]$2.30[\/latex] per hour. Assume the minimum wage grows according to an exponential model where [latex]n[\/latex] represents the time in years after 1960.\n
                                                            \n
                                                          1. Find an explicit formula for the minimum wage.<\/li>\n
                                                          2. What does the model predict for the minimum wage in 1960?<\/li>\n
                                                          3. If the minimum wage was [latex]$5.15[\/latex] in 1996, is this above, below or equal to what the model predicts?<\/li>\n<\/ol>\n<\/li>\n
                                                          4. The population of a small town can be described by the equation [latex]P_n = 4000+70n[\/latex], where [latex]n[\/latex] is the number of years after 2005. Explain in words what this equation tells us about how the population is changing.<\/li>\n
                                                          5. The population of a small town can be described by the equation [latex]P_n = 4000(1.04)n[\/latex], where [latex]n[\/latex] is the number of years after 2005. Explain in words what this equation tells us about how the population is changing.<\/li>\n
                                                          6. A new truck costs [latex]$32,000[\/latex]. The car\u2019s value will depreciate over time, which means it will lose value. For tax purposes, depreciation is usually calculated linearly. If the truck is worth [latex]$24,500[\/latex] after three years, write an explicit formula for the value of the car after [latex]n[\/latex] years.<\/li>\n
                                                          7. Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying, “In my day, you could buy a cup of coffee for a nickel”). Suppose inflation decreases the value of money by [latex]5\\%[\/latex] each year. In other words, if you have [latex]$1[\/latex] this year, next year it will only buy you [latex]$0.95[\/latex] worth of stuff. How much will [latex]$100[\/latex] buy you in [latex]20[\/latex] years?<\/li>\n
                                                          8. Suppose that you have a bowl of [latex]500[\/latex] M&M candies, and each day you eat [latex]\\frac{1}{4}[\/latex] of the candies you have. Is the number of candies left changing linearly or exponentially? Write an equation to model the number of candies left after [latex]n[\/latex] days.<\/li>\n
                                                          9. A warm object in a cooler room will decrease in temperature exponentially, approaching the room temperature according to the formula where [latex]T_n[\/latex] is the temperature after [latex]n[\/latex] minutes, [latex]r[\/latex] is the rate at which temperature is changing, [latex]a[\/latex] is a constant, and [latex]Tr[\/latex] is the temperature of the room. Forensic investigators can use this to predict the time of death of a homicide victim. Suppose that when a body was discovered [latex](n=0)[\/latex] it was [latex]85[\/latex] degrees. After [latex]20[\/latex] minutes, the temperature was measured again to be [latex]80[\/latex] degrees. The body was in a [latex]70[\/latex] degree room.\n
                                                              \n
                                                            1. Use the given information with the formula provided to find a formula for the temperature of the body.<\/li>\n
                                                            2. When did the victim die, if the body started at [latex]98.6[\/latex] degrees?<\/li>\n<\/ol>\n<\/li>\n
                                                            3. Recursive equations can be very handy for modeling complicated situations for which explicit equations would be hard to interpret. As an example, consider a lake in which 2000 fish currently reside. The fish population grows by [latex]10\\%[\/latex] each year, but every year [latex]100[\/latex] fish are harvested from the lake by people fishing.\n
                                                                \n
                                                              1. Write a recursive equation for the number of fish in the lake after [latex]n[\/latex] years.<\/li>\n
                                                              2. Calculate the population after [latex]1[\/latex] and [latex]2[\/latex] years. Does the population appear to be increasing or decreasing?<\/li>\n
                                                              3. What is the maximum number of fish that could be harvested each year without causing the fish population to decrease in the long run?<\/li>\n<\/ol>\n<\/li>\n
                                                              4. The number of Starbucks stores grew after first opened. The number of stores from 1990-2007, as reported on their corporate website[1]<\/sup><\/a>, is shown below.\n
                                                                  \n
                                                                1. Carefully plot the data. Does is appear to be changing linearly or exponentially?<\/li>\n
                                                                2. Try finding an equation to model the data by picking two points to work from. How well does the equation model the data?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                                  \"clipboard_e723972894bc819360fb5aa9fe3e212fd.png\"<\/p>\n

                                                                    \n
                                                                  1. Thomas Malthus was an economist who put forth the principle that population grows based on an exponential growth model, while food and resources grow based on a linear growth model. Based on this, Malthus predicted that eventually demand for food and resources would out outgrow supply, with doom-and-gloom consequences. Do some research about Malthus to answer these questions.\n
                                                                      \n
                                                                    1. What societal changes did Malthus propose to avoid the doom-and-gloom outcome he was predicting?<\/li>\n
                                                                    2. Why do you think his predictions did not occur?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n
                                                                      1. https:\/\/stories.starbucks.com\/uploads\/2019\/01\/AboutUs-Company-Timeline-1.6.21-FINAL.pdf ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":15,"menu_order":25,"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":"practice","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\/8440"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8440\/revisions"}],"predecessor-version":[{"id":15478,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8440\/revisions\/15478"}],"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\/8440\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8440"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8440"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8440"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}