{"id":"cb_question_bank:9495f164-54e1-408c-81b0-ccad66bb1132","source_id":"cb_question_bank","source_item_id":"9495f164-54e1-408c-81b0-ccad66bb1132","external_id":null,"ibn":"025038-DC","question_id":"281a4f3b","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, f of x , and the number of years after 2015, x ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2%&nbsp;less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/26d9f477bb154c8ef7637e64827776ac5831aa760a31d21a53157367bd210b16\" alt=\"f of x\"></span>, and the number of years after 2015, <span class=\"italic\">x</span>&nbsp;?</p>\n","rationale_html":"<p>Choice D is correct. Because the change in the number of students decreases by the same percentage each year, the relationship between the number of students and the number of years can be modeled with a decreasing exponential function in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/62734c2968165aa1424c54d847020cd31d195e4fb2e232a52405f79339ac8519\" alt=\"f of x equals, a, times, open parenthesis, 1 minus r, close parenthesis, to the x power \"></span>, where <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/83e40a9d411886c8f1db15daf1bfe1768471306e4f8f1a8978edff12e6c8e9e5\" alt=\"f of x \"></span> is the number of students, <span class=\"italic\">a</span> is the number of students in 2015, <span class=\"italic\">r</span> is the rate of decrease each year, and <span class=\"italic\">x</span> is the number of years since 2015. It’s given that 3,000 students were enrolled in 2015 and that the rate of decrease is predicted to be 2%, or 0.02. Substituting these values into the decreasing exponential function yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dc68108f1cba2e79bf8ccc60adb007744af5958772ee9c305bc9f1b1d4353ff6\" alt=\"f of x equals, 3,000 times, open parenthesis, 1 minus 0 point 0 2, close parenthesis, to the x power\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0371ccb1cee2489b69db397b2f418ec7f7c884c2574be519e7a979fe7fa24282\" alt=\"f of x equals, 3,000 times, open parenthesis, 0 point 9 8, close parenthesis, to the x power\"></span>.</p><p>Choices A, B, and C are incorrect and may result from conceptual errors when translating the given information into a decreasing exponential function.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.618000+00:00","source_updated_at":"2023-08-02T20:25:59.618000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/20eeaae44da350081b092bb40f6ebfec8d69f589b168c232a3ede09c263c04c6\" alt=\"f of x equals, 0 point 0 2, times open parenthesis, 3,000, close parenthesis, to the x power\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3c07f9bd7ef91befdb8d4fbb4260312a99f3b57223f59bdcde206b2f006d649c\" alt=\"f of x equals, 0 point 9 8, times open parenthesis, 3,000, close parenthesis, to the x power\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/57fba5549144a00d1ffcbd3c4402edaff9b83e2f259a23a52fb0110b0f66073f\" alt=\"f of x equals, 3,000, times open parenthesis, 0 point 0 2, close parenthesis, to the x power\"></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4969586f0df1ba1cac3304c3d9b466db8728481888e82b8b280d9cd9679dfe71\" alt=\"f of x equals, 3,000, times open parenthesis, 0 point 9 8, close parenthesis, to the x power, \"></span></span>\n          </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}}