{"id":"cb_question_bank:b1474e42-6ba5-45fc-83b0-e06d764badb4","source_id":"cb_question_bank","source_item_id":"b1474e42-6ba5-45fc-83b0-e06d764badb4","external_id":"e10027a7-cac8-4ca2-855a-ca3f00b55687","ibn":null,"question_id":"4209aefe","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 f left parenthesis x right parenthesis equals 206 left parenthesis 1.034 right parenthesis Superscript x models the value, in dollars, of a certain bank account by the end of each year from 1957 through 1972 , where x is the number of years after 1957 . Which of the following is the best interpretation of “ f left parenthesis 5 right parenthesis is approximately equal to 243 ” in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The function <math alttext=\"f left parenthesis x right parenthesis equals 206 left parenthesis 1.034 right parenthesis Superscript x\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mn>206</mn></mrow><msup><mrow><mo>(</mo><mrow><mn>1.034</mn></mrow><mo>)</mo></mrow><mi>x</mi></msup></math> models the value, in dollars, of a certain bank account by the end of each year from <math alttext=\"1957\"><mn>1957</mn>\n</math> through <math alttext=\"1972\"><mn>1972</mn>\n</math>, where <math alttext=\"x\"><mi>x</mi>\n</math> is the number of years after <math alttext=\"1957\"><mn>1957</mn>\n</math>. Which of the following is the best interpretation of “<math alttext=\"f left parenthesis 5 right parenthesis\"><mi>f</mi><mo>(</mo><mrow><mn>5</mn></mrow><mo>)</mo></math> is approximately equal to <math alttext=\"243\"><mn>243</mn>\n</math>” in this context?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. It’s given that the function <math alttext=\"f left parenthesis x right parenthesis equals 206 left parenthesis 1.034 right parenthesis Superscript x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>206</mn><msup><mfenced><mn>1.034</mn></mfenced><mi>x</mi></msup></math> models the value, in dollars, of a certain bank account by the end of each year from <math alttext=\"19 57\"><mn>19</mn>\n<mn>57</mn>\n</math> through <math alttext=\"19 72\"><mn>19</mn>\n<mn>72</mn>\n</math>, where <math alttext=\"x\"><mi>x</mi>\n</math> is the number of years after <math alttext=\"19 57\"><mn>19</mn>\n<mn>57</mn>\n</math>. It follows that&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> represents the estimated value, in dollars, of the bank account <math alttext=\"x\"><mi>x</mi>\n</math> years after <math alttext=\"19 57\"><mn>19</mn>\n<mn>57</mn>\n</math>. Since the value of&nbsp;<math alttext=\"f left parenthesis 5 right parenthesis\"><mi>f</mi><mfenced><mn>5</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 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>, it follows that “<math alttext=\"f left parenthesis 5 right parenthesis\"><mi>f</mi><mfenced><mn>5</mn></mfenced></math> is approximately equal to <math alttext=\"243\"><mn>243</mn>\n</math>” means that&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is approximately equal to <math alttext=\"243\"><mn>243</mn>\n</math> when <math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>. In the given context, this means that the value of the bank account is estimated to be approximately <math alttext=\"243\"><mn>243</mn>\n</math> dollars <math alttext=\"5\"><mn>5</mn>\n</math> years after <math alttext=\"19 57\"><mn>19</mn>\n<mn>57</mn>\n</math>. Therefore, the best interpretation of the statement “<math alttext=\"f left parenthesis 5 right parenthesis\"><mi>f</mi><mfenced><mn>5</mn></mfenced></math> is approximately equal to <math alttext=\"243\"><mn>243</mn>\n</math>” in this context is the value of the bank account is estimated to be approximately <math alttext=\"243\"><mn>243</mn>\n</math> dollars in <math alttext=\"19 62\"><mn>19</mn>\n<mn>62</mn>\n</math>.</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 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":["B"],"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 value of the bank account is estimated to be approximately <math alttext=\"5\"><mn>5</mn>\n</math> dollars greater in <math alttext=\"1962\"><mn>1962</mn>\n</math> than in <math alttext=\"1957\"><mn>1957</mn>\n</math>.</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">The value of the bank account is estimated to be approximately <math alttext=\"243\"><mn>243</mn>\n</math> dollars in <math alttext=\"1962\"><mn>1962</mn>\n</math>.</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">The value, in dollars, of the bank account is estimated to be approximately <math alttext=\"5\"><mn>5</mn>\n</math> times greater in <math alttext=\"1962\"><mn>1962</mn>\n</math> than in <math alttext=\"1957\"><mn>1957</mn>\n</math>.</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">The value of the bank account is estimated to increase by approximately <math alttext=\"243\"><mn>243</mn>\n</math> dollars every <math alttext=\"5\"><mn>5</mn>\n</math> years between <math alttext=\"1957\"><mn>1957</mn>\n</math> and <math alttext=\"1972\"><mn>1972</mn>\n</math>.</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}}