{"id":"cb_question_bank:78dac9d1-a684-4426-a2e9-6ee8da9d80e9","source_id":"cb_question_bank","source_item_id":"78dac9d1-a684-4426-a2e9-6ee8da9d80e9","external_id":null,"ibn":"09384-DC","question_id":"16889ef3","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year 2000?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Oil and gas production in a certain area dropped from 4&nbsp;million&nbsp;barrels in 2000 to 1.9&nbsp;million&nbsp;barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions <span class=\"italic\">f</span> best models the production, in millions of barrels, <span class=\"italic\">t</span> years after the year 2000?</p>\n","rationale_html":"<p>Choice C is correct. It is assumed that the oil and gas production decreased at a constant rate. Therefore, the function <span class=\"italic\">f </span>that best models the production <span class=\"italic\">t</span> years after the year 2000 can be written as a linear function, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c0559d94de7204622922c5ca25ec9f0e3e64f047dd2b77d5d91b860a6250dc27\" alt=\"f of t equals, m, t plus b\"></span>, where <span class=\"italic\">m</span> is the rate of change of the oil and gas production and <span class=\"italic\">b </span>is the oil and gas production, in millions of barrels, in the year 2000. Since there were 4 million barrels of oil and gas produced in 2000, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b02a2759ca9b08a9fcebf050ff7910b4388068d8bd17f6a556f9cd3d26eddf2b\" alt=\"b equals 4\"></span>. The rate of change, <span class=\"italic\">m</span>, can be calculated as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0ff0a9a2be5f537834b9b87bdf0e593311e113e06dfe563a7a4edc077f047595\" alt=\"the fraction with numerator 4 minus 1 point 9, and denominator 0 minus 13, end fraction, equals, the negative of the fraction 2 point 1 over 13\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0b597f4d41ff238a3b0431ffaddb2cc5a9a375abd067ba80027f7de2f0817fab\" alt=\"the negative of the fraction 21 over 130\"></span>, the rate of change in choice C.</p><p>Choices A and B are incorrect because each of these functions has a positive rate of change. Since the oil and gas production decreased over time, the rate of change must be negative. Choice D is incorrect. This model may result from misinterpreting 1.9 million barrels as the amount by which the production decreased.</p><p></p>\n","correct_answer":["C"],"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_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/315504aaa350a92e7b8c1ba7eb73f9369d7a90944ef7b5887cb6cd13f9a5c792\" alt=\"f of t equals, the fraction 21 over 130, end fraction, t plus 4\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/886bdc728aff2d7ba8d0ff8c9106a601bb75a9cdc634907079edec2bf37ee2f6\" alt=\"f of t equals, the fraction 19 over 130, end fraction, t plus 4\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d040d4b2326b9df87105b3415e441d08cb34389e64bdaf81209b82d67877c122\" alt=\"f of t equals, the negative fraction 21 over 130, end fraction, t plus 4\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c3c0347fc79fcbb68a9fc048d5e7774638d1e8f5144f27ff5e60bd13e04bd023\" alt=\"f of t equals, the negative fraction 19 over 130, end fraction, t plus 4\"></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}}