{"id":"cb_question_bank:9406cedc-7041-4013-ba2f-338ee94bb04e","source_id":"cb_question_bank","source_item_id":"9406cedc-7041-4013-ba2f-338ee94bb04e","external_id":null,"ibn":"019576-DC","question_id":"59d1f4b5","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The equation above models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years after the gym opens?","stimulus":"M equals 1,800 times, 1 point 0 2, to the power t","stimulus_html":"<div class=\"stimulus_reference \">\n\t<p class=\"standalone_statement style:1 \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/73bb57967469e9bd0a9ae2b7638545e000c82de04070b21c7f99cdc93e3aab08\" alt=\"M equals 1,800 times, 1 point 0 2, to the power t\"></span></span></p>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">The equation above models the number of members,&nbsp;<span class=\"italic\">M,</span> of a gym <span class=\"italic\">t</span> years after the gym opens. Of the following, which equation models the number of members of the gym <span class=\"italic\">q</span> quarter years after the gym opens?</p>\n","rationale_html":"<p>Choice A is correct. In 1 year, there are 4 quarter years, so the number of quarter years, <span class=\"italic\">q</span>, is 4 times the number of years, <span class=\"italic\">t</span> ; that is, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5a3410b1eb993d1b797e481e8c7ca572c79ef27756b9598fe35851e8c10ae34e\" alt=\"q, equals 4, t\"></span>. This is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/be213684f1b271436c97e7a80635e07a9ed72becff70a44bc51950f1d1316f4b\" alt=\" t equals, q over 4\"></span>, and substituting this into the expression for <span class=\"italic\">M</span> in terms of <span class=\"italic\">t</span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e1246042d7f16fecc3a742767a7b2ba1a5c66cf92c41f8d1e4f3a67237193bbb\" alt=\"M equals, 1,800 times, 1 point 0 2 raised to the fraction q over 4 power\"></span>.</p><p>Choices B and D are incorrect and may be the result of incorrectly using <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8e31e89f222f88a30f84a3e35ac9029983ae21e89a9562962302924720e20bf3\" alt=\"t equals, 4 q\"></span> instead of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5a3410b1eb993d1b797e481e8c7ca572c79ef27756b9598fe35851e8c10ae34e\" alt=\"q, equals 4, t\"></span>. (Choices B and D are nearly the same since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/88c7ea44cd0cad3f52fca72b8ebb95da3de0c27145f68bc15497d62f77ffc37e\" alt=\"1 point 0 2 raised to the 4 q power\"></span> is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4d7b79b095158daea5e339555cd275e0bd1670a823e1255fa6ac5862b92110c2\" alt=\"open parenthesis, 1 point 0 2 to the fourth power, close parenthesis, raised to the q power\"></span>, which is approximately <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b0f156f2b22184baed71595312301eb983ba7291049edf2c0fbd1a54c8d78f91\" alt=\"1 point 0 8 2 to the q power\"></span>.) Choice C is incorrect and may be the result of incorrectly using <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8e31e89f222f88a30f84a3e35ac9029983ae21e89a9562962302924720e20bf3\" alt=\"t equals, 4 q\"></span>&nbsp;and unnecessarily dividing 0.02 by 4.</p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.616000+00:00","source_updated_at":"2023-08-02T20:25:59.616000+00:00","options":[{"label":"A","content_html":"<p><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e1246042d7f16fecc3a742767a7b2ba1a5c66cf92c41f8d1e4f3a67237193bbb\" alt=\"M equals 1,800 times, 1 point 0 2, to the power of the fraction q over 4\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/965ee972551810b7e04bea35db1ffcb334de8064e4b055e64265669226496ebf\" alt=\"M equals 1,800 times, 1 point 0 2, to the power 4 q\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3f29bd8ba4a059a7df14ffb52adb5e741210e8bbd67b5c084f24f3748ebbf42e\" alt=\"M equals 1,800 times, 1 point 0 0 5, to the power 4 q\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2d2f3e3ec804649d5a6c720521b29f3eb48eb6feeacedc7023a04d835e66921c\" alt=\"M equals 1,800 times, 1 point 0 8 2, to the power q\"></span></span></p>\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}}