{"id":"cb_question_bank:4cfb040c-106b-4f65-9d70-c9d734a128d9","source_id":"cb_question_bank","source_item_id":"4cfb040c-106b-4f65-9d70-c9d734a128d9","external_id":"d73707f3-c5fe-430b-8799-06ef95532995","ibn":null,"question_id":"be0c419e","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":"Immanuel purchased a certain rare coin on January 1. The function f left parenthesis x right parenthesis equals 65 left parenthesis 1.03 right parenthesis Superscript x , where 0 less than or equals x less than or equals 10 , gives the predicted value, in dollars, of the rare coin x years after Immanuel purchased it. What is the best interpretation of the statement “ f left parenthesis 8 right parenthesis is approximately equal to 82 ” in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Immanuel purchased a certain rare coin on January 1. The function <math alttext=\"f left parenthesis x right parenthesis equals 65 left parenthesis 1.03 right parenthesis Superscript x\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>65</mn><msup><mfenced><mn>1.03</mn></mfenced><mi>x</mi></msup></math>, where&nbsp;<math alttext=\"0 less than or equals x less than or equals 10\"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>10</mn></math>, gives the predicted value, in dollars, of the rare coin <math alttext=\"x\"><mi>x</mi>\n</math> years after Immanuel purchased it. What is the best interpretation of the statement “<math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced></math> is approximately equal to <math alttext=\"82\"><mn>82</mn>\n</math>” in this context?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. It’s given that the function <math alttext=\"f left parenthesis x right parenthesis equals 65 left parenthesis 1.03 right parenthesis Superscript x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>65</mn><msup><mfenced><mn>1.03</mn></mfenced><mi>x</mi></msup></math> gives the predicted value, in dollars, of a certain rare coin <math alttext=\"x\"><mi>x</mi>\n</math> years after Immanuel purchased it. It follows that <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> represents the predicted value, in dollars, of the coin <math alttext=\"x\"><mi>x</mi>\n</math> years after Immanuel purchased it. Since the value of <math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced></math> is the value of <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> when <math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math>, it follows that “<math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced></math> is approximately equal to <math alttext=\"82\"><mn>82</mn>\n</math>” means that <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is approximately equal to <math alttext=\"82\"><mn>82</mn>\n</math> when <math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math>. Therefore, the best interpretation of the statement “<math alttext=\"f left parenthesis 8 right parenthesis\"><mi>f</mi><mfenced><mn>8</mn></mfenced></math> is approximately equal to <math alttext=\"82\"><mn>82</mn>\n</math>” in this context is <math alttext=\"8\"><mn>8</mn>\n</math> years after Immanuel purchased the rare coin, its predicted value is approximately <math alttext=\"82\"><mn>82</mn>\n</math> dollars.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual errors.</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>","correct_answer":["D"],"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;\">When the rare coin's predicted value is approximately <math alttext=\"82\"><mn>82</mn>\n</math> dollars, it is <math alttext=\"8 percent sign\"><mn>8</mn>\n<mo>%</mo></math> greater than the predicted value, in dollars, on January 1 of the previous year.</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">When the rare coin’s predicted value is approximately <math alttext=\"82\"><mn>82</mn>\n</math> dollars, it is <math alttext=\"8\"><mn>8</mn>\n</math> times the predicted value, in dollars, on January 1 of the previous year.</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">From the day Immanuel purchased the rare coin to <math alttext=\"8\"><mn>8</mn>\n</math> years after Immanuel purchased the coin, its predicted value increased by a total of approximately <math alttext=\"82\"><mn>82</mn>\n</math> dollars.</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\"><math alttext=\"8\"><mn>8</mn>\n</math> years after Immanuel purchased the rare coin, its predicted value is approximately <math alttext=\"82\"><mn>82</mn>\n</math> dollars.</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}}