{"id":"cb_question_bank:cc8ca5b9-419e-44c3-b7eb-66ce53cb83b4","source_id":"cb_question_bank","source_item_id":"cc8ca5b9-419e-44c3-b7eb-66ce53cb83b4","external_id":"8472776c-becb-4a82-bf1b-aa29eb25da77","ibn":null,"question_id":"b7cd6ca6","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 equation upper E left parenthesis t right parenthesis equals 5 left parenthesis 1.8 right parenthesis Superscript t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The equation&nbsp;<math alttext=\"upper E left parenthesis t right parenthesis equals 5 left parenthesis 1.8 right parenthesis Superscript t\"><mi>E</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>5</mn><msup><mfenced><mn>1.8</mn></mfenced><mi>t</mi></msup></math> gives the estimated number of employees at a restaurant, where <math alttext=\"t\"><mi>t</mi>\n</math> is the number of years since the restaurant opened. Which of the following is the best interpretation of the number <math alttext=\"5\"><mn>5</mn>\n</math> in this context?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. For an exponential function of the form <math alttext=\"upper E left parenthesis t right parenthesis equals a left parenthesis b right parenthesis Superscript t\"><mi>E</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>a</mi><msup><mfenced><mi>b</mi></mfenced><mi>t</mi></msup></math>, where <math alttext=\"a\"><mi>a</mi>\n</math> and <math alttext=\"b\"><mi>b</mi>\n</math> are constants, the initial value of the function—that is, the value of the function when <math alttext=\"t equals 0\"><mrow>\n\t<mi>t</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>—is <math alttext=\"a\"><mi>a</mi>\n</math> and the value of the function increases by a factor of <math alttext=\"b\"><mi>b</mi>\n</math> each time <math alttext=\"t\"><mi>t</mi>\n</math> increases by <math alttext=\"1\"><mn>1</mn>\n</math>. Since the function <math alttext=\"upper E left parenthesis t right parenthesis equals 5 left parenthesis 1.8 right parenthesis Superscript t\"><mi>E</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>5</mn><msup><mfenced><mn>1.8</mn></mfenced><mi>t</mi></msup></math> gives the estimated number of employees at a restaurant and <math alttext=\"t\"><mi>t</mi>\n</math> is the number of years since the restaurant opened, the best interpretation of the number <math alttext=\"5\"><mn>5</mn>\n</math> in this context is the estimated number of employees when <math alttext=\"t equals 0\"><mrow>\n\t<mi>t</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>, or when the restaurant opened.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.826000+00:00","source_updated_at":"2023-08-02T20:25:59.826000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">The estimated number of employees when the restaurant opened</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">The increase in the estimated number of employees each year</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">The number of years the restaurant has been open</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">The percent increase in the estimated number of employees each year</p>","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}}