{"id":"cb_question_bank:f6c61b14-6792-46ab-901a-3e83d20b5fbf","source_id":"cb_question_bank","source_item_id":"f6c61b14-6792-46ab-901a-3e83d20b5fbf","external_id":null,"ibn":"10521-DC","question_id":"41fdc0b8","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The figure presents a 2-column table, with two rows of data, titled “Population of Greenleaf, Idaho.” The heading of the first column is “Year.” The heading of the second column is “Population.” The 2 rows of data are as follows. Row 1. Year, 2000. Population, 862. Row 2. Year, 2010. Population, 846 The table above shows the population of Greenleaf, Idaho, for the years 2000 and 2010. If the relationship between population and year is linear, which of the following functions P models the population of Greenleaf t years after 2000?","stimulus":"","stimulus_html":null,"stem_html":"<p><img src=\"/api/assets/09d2b73db60258b26616bf5bae1c1f9187bf67d98c4446e106148fbc5eaa87be\" alt=\"The figure presents a 2-column table, with two rows of data, titled “Population of Greenleaf, Idaho.” The heading of the first column is “Year.” The heading of the second column is “Population.” The 2 rows of data are as follows. Row 1. Year, 2000. Population, 862. Row 2. Year, 2010. Population, 846\n\" width=\"129\" height=\"74\"></p><p>The table above shows the population of Greenleaf, Idaho, for the years 2000 and 2010. If the relationship between population and year is linear, which of the following functions <span class=\"italic\">P</span> models the population of Greenleaf <span class=\"italic\">t</span> years after 2000?</p><p></p>\n","rationale_html":"<p>Choice A is correct. It is given that the relationship between population and year is linear; therefore, the function that models the population <span class=\"italic\">t</span> years after 2000 is of the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7c74bbbc6db79018f8e8136902ccf6270e006f5ab317bf27a79ed0815c817ff0\" alt=\"P of t equals, m, t plus b\"></span>, where <span class=\"italic\">m</span> is the slope and <span class=\"italic\">b</span> is the population when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03be3f9ca86e73f91aae3da5f4c70ddbd7015f7b2182c3cada4a3b84a54d9546\" alt=\"t equals 0\"></span>. In the year 2000, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03be3f9ca86e73f91aae3da5f4c70ddbd7015f7b2182c3cada4a3b84a54d9546\" alt=\"t equals 0\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cbc25f8d390f8bded17743a039526c59a35f22880454e6841a605a6546930322\" alt=\"b equals 862\"></span>. The slope is given by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bb2e6ac15f66cc0cdf5253270d85b873ca8ca7b632d5dd475a164a0b8256d46c\" alt=\"m equals, the fraction with numerator P of 10, minus P of 0, and denominator 10 minus 0, end fraction, which equals the fraction with numerator 846 minus 862, and denominator 10 minus 0, end fraction, which equals negative 16 over 10, which equals negative 1 point 6\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e93e9a7a60046a542450ced96279d43047ff7b43b7b61f694a127cbe24964950\" alt=\"P of t equals, negative 1 point 6, t, plus 862\"></span>, which is equivalent to the equation in choice A.</p><p>Choice B is incorrect and may be the result of incorrectly calculating the slope as just the change in the value of <span class=\"italic\">P</span>. Choice C is incorrect and may be the result of the same error as in choice B, in addition to incorrectly using <span class=\"italic\">t</span> to represent the year, instead of the number of years after 2000. Choice D is incorrect and may be the result of incorrectly using <span class=\"italic\">t</span> to represent the year instead of the number of years after 2000.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/383b5428b6d21992dc9ce3ddd365516bad09b3a75c36d352744f7f80bed58881\" alt=\"P of t equals, 862 minus 1 point 6 times t\"></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/16bd19504df8eb3901377dec9c7c12e6fb7b6bdd211974f4c4ae6e8df95e84f7\" alt=\"P of t equals, 862 minus 16 times t\"></span>\n","ord":1},{"label":"C","content_html":"<span class=\"italic\">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1b6bc9217ef3a858518227638d0eed330629db4e72ace545ec3ba2bef90bd66c\" alt=\"P of t equals, 862 plus 16 times, open parenthesis, t minus 2,000, close parenthesis\"></span><span class=\"italic\"></span><span class=\"italic\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"italic\"><span class=\"italic\"></span><span class=\"italic\"></span><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/62eb80521e13e20e1e5ca50de53e4ea7ca6f02f71af6fb1d8074cfc8bd0b5627\" alt=\"P of t equals, 862 minus 1 point 6 times, open parenthesis, t minus 2,000, close parenthesis\"></span></span>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}