{"id":"cb_question_bank:dfd097b9-9927-4fa3-bc1c-db2b1b3491e8","source_id":"cb_question_bank","source_item_id":"dfd097b9-9927-4fa3-bc1c-db2b1b3491e8","external_id":"25d9ebe8-a480-4c88-9e5d-9b4803a4780c","ibn":null,"question_id":"08d03fe4","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"For the exponential function f , the value of f left parenthesis 1 right parenthesis is k , where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">For the exponential function <math alttext=\"f\"><mi>f</mi>\n</math>, the value of&nbsp;<math alttext=\"f left parenthesis 1 right parenthesis\"><mi>f</mi><mfenced><mn>1</mn></mfenced></math> is <math alttext=\"k\"><mi>k</mi>\n</math>, where <math alttext=\"k\"><mi>k</mi>\n</math> is a constant. Which of the following equivalent forms of the function <math alttext=\"f\"><mi>f</mi>\n</math> shows the value of <math alttext=\"k\"><mi>k</mi>\n</math> as the coefficient or the base?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. For the form of the function in choice C, <math alttext=\"f left parenthesis x right parenthesis equals 128 left parenthesis 1.6 right parenthesis Superscript x minus 1\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>128</mn><msup><mfenced><mn>1.6</mn></mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></msup></math>, the value of <math alttext=\"f left parenthesis 1 right parenthesis\"><mi>f</mi><mfenced><mn>1</mn></mfenced></math> can be found as <math alttext=\"128 left parenthesis 1.6 right parenthesis Superscript 1 minus 1\"><mn>128</mn><msup><mfenced><mn>1.6</mn></mfenced><mrow><mn>1</mn><mo>-</mo><mn>1</mn></mrow></msup></math>, which is equivalent to&nbsp;<math alttext=\"128 left parenthesis 1.6 right parenthesis Superscript 0\"><mn>128</mn><msup><mfenced><mn>1.6</mn></mfenced><mn>0</mn></msup></math>, or <math alttext=\"128\"><mn>128</mn>\n</math>. Therefore, <math alttext=\"k equals 128\"><mrow>\n\t<mi>k</mi>\n\t<mo>=</mo>\n\t<mn>128</mn>\n</mrow>\n</math>, which is shown in <math alttext=\"f left parenthesis x right parenthesis equals 128 left parenthesis 1.6 right parenthesis Superscript x minus 1\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>128</mn><msup><mfenced><mn>1.6</mn></mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></msup></math> as the coefficient.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.828000+00:00","source_updated_at":"2023-08-02T20:25:59.828000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals 50 left parenthesis 2 right parenthesis Superscript x plus 1\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>50</mn></mrow><msup><mfenced><mrow><mn>2</mn></mrow></mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals 80 left parenthesis 2 right parenthesis Superscript x\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>80</mn></mrow><msup><mfenced><mrow><mn>2</mn></mrow></mfenced><mi>x</mi></msup></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals 128 left parenthesis 2 right parenthesis Superscript x minus 1\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>128</mn></mrow><msup><mfenced><mrow><mn>2</mn></mrow></mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></msup></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"f left parenthesis x right parenthesis equals 205 left parenthesis 2 right parenthesis Superscript x minus 2\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>205</mn></mrow><msup><mfenced><mrow><mn>2</mn></mrow></mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></msup></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}}