{"id":"cb_question_bank:22db4118-7ecf-4e07-9ba3-249db70d4fb4","source_id":"cb_question_bank","source_item_id":"22db4118-7ecf-4e07-9ba3-249db70d4fb4","external_id":null,"ibn":"029350-DC","question_id":"e53add44","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":"The function S above models the annual salary, in dollars, of an employee n years after starting a job, where a is a constant. If the employee’s salary increases by 4% each year, what is the value of a ?","stimulus":"S of n, equals, 38,000 times a, to the n power","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a08f2e1b36f08bc678b3986cd4bebaa78012ab31f0497904b116a5cb247619eb\" alt=\"S of n, equals, 38,000 times a, to the n power\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The function <span class=\"italic\">S</span> above models the annual salary, in dollars, of an employee <span class=\"italic\">n</span> years after starting a job, where <span class=\"italic\">a</span> is a constant. If the employee’s salary increases by 4% each year, what is the value of <span class=\"italic\">a </span>?</p>\n","rationale_html":"<p>Choice C is correct. A model for a quantity <span class=\"italic\">S</span> that increases by a certain percentage per time period <span class=\"italic\">n</span> is an exponential function in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/806f1a7f51524deae5a3fe0f6e09e664ae26a29e438e9bef2b67fa22be5ed651\" alt=\"S of n equals, I times, open parenthesis, 1 plus r over 100, close parenthesis, to the n power\"></span>, where <span class=\"italic\">I</span> is the initial value at time <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/00d80cbcfc147f279899302462515719406efaf8a3ec0771a18cfef1f412db3e\" alt=\"n equals 0 \"></span> for <span class=\"italic\">r</span>% annual increase. It’s given that the annual increase in an employee’s salary is 4%, so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/53bc3ba958540b28271940f9688528f6613e474ef3999ec9a6b6ed475924528a\" alt=\"r equals 4\"></span>. The initial value can be found by substituting 0 for <span class=\"italic\">n</span> in the given function, which yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e881bb105a4fdb5b847ce2327b2fc17eeb1146a09e1ed7cd92d6ef6fce24f33a\" alt=\"S of 0 equals 38,000\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a0024238d68e7b9eeecf54459cd0e9851266e692cf8815a24d43916da39240f7\" alt=\"I equals 38,000\"></span>. Substituting these values for <span class=\"italic\">r</span> and <span class=\"italic\">I</span> into the form of the exponential function <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/806f1a7f51524deae5a3fe0f6e09e664ae26a29e438e9bef2b67fa22be5ed651\" alt=\"S of n equals, I times, open parenthesis, 1 plus r over 100, close parenthesis, to the n power\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/02aa2a8b022c7575b2d0502e7a739b934e676246cb24984cf2b6c55c25ce8cd3\" alt=\"S of n equals, 38,000 times, open parenthesis, 1 plus 4 over 100, close parenthesis, to the n power\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c40a476b52a66ce1e8704a8e998d9763d1e4d9befaebe6fa2d723a4cc841aa04\" alt=\"S of n equals, 38,000 times, 1 point 0 4 to the n power\"></span>. Therefore, the value of <span class=\"italic\">a</span> in the given function is 1.04.</p><p>Choices A, B, and D are incorrect and may result from incorrectly representing the annual increase in the exponential function.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.624000+00:00","source_updated_at":"2023-08-02T20:25:59.624000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">0.04</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">0.4</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">1.04</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">1.4</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}}