{"id":"cb_question_bank:de014676-64eb-4582-889b-bd3f3cf97a59","source_id":"cb_question_bank","source_item_id":"de014676-64eb-4582-889b-bd3f3cf97a59","external_id":"fb591f40-b171-470c-ab62-48c9c0ee004b","ibn":null,"question_id":"1fe10d97","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"p left parenthesis t right parenthesis equals 90,000 left parenthesis 1.06 right parenthesis Superscript t The given function p models the population of Lowell t years after a census. Which of the following functions best models the population of Lowell m months after the census?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"p left parenthesis t right parenthesis equals 90,000 left parenthesis 1.06 right parenthesis Superscript t\"><mi>p</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>90,000</mn><msup><mfenced><mn>1.06</mn></mfenced><mi>t</mi></msup></math></p>\n<p>The given function <math alttext=\"p\"><mi>p</mi>\n</math> models the population of Lowell&nbsp;<math alttext=\"t\"><mi>t</mi>\n</math> years after a census. Which of the following functions best models the population of Lowell&nbsp;<math alttext=\"m\"><mi>m</mi>\n</math> months after the census?</p>","rationale_html":"<p>Choice D is correct. It’s given that the function <math alttext=\"p\"><mi>p</mi>\n</math> models the population of Lowell <math alttext=\"t\"><mi>t</mi>\n</math> years after a census. Since there are <math alttext=\"12\"><mn>12</mn>\n</math> months in a year, <math alttext=\"m\"><mi>m</mi>\n</math> months after the census is equivalent to&nbsp;<math alttext=\"StartFraction m Over 12 EndFraction\"><mfrac><mi>m</mi><mn>12</mn></mfrac></math> years after the census. Substituting <math alttext=\"StartFraction m Over 12 EndFraction\"><mfrac><mi>m</mi><mn>12</mn></mfrac></math> for <math alttext=\"t\"><mi>t</mi>\n</math> in the equation&nbsp;<math alttext=\"p left parenthesis t right parenthesis equals 90,000 left parenthesis 1.06 right parenthesis Superscript t\"><mi>p</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>90,000</mn><msup><mfenced><mn>1.06</mn></mfenced><mi>t</mi></msup></math> yields <math alttext=\"p left parenthesis StartFraction m Over 12 EndFraction right parenthesis equals 90,000 left parenthesis 1.06 right parenthesis Superscript StartFraction m Over 12 EndFraction\"><mi>p</mi><mfenced><mfrac><mi>m</mi><mn>12</mn></mfrac></mfenced><mo>=</mo><mn>90,000</mn><msup><mfenced><mn>1.06</mn></mfenced><mfrac><mi>m</mi><mn>12</mn></mfrac></msup></math>. Therefore, the function <math alttext=\"r\"><mi>r</mi>\n</math> that best models the population of Lowell <math alttext=\"m\"><mi>m</mi>\n</math> months after the census is <math alttext=\"r left parenthesis m right parenthesis equals 90,000 left parenthesis 1.06 right parenthesis Superscript StartFraction m Over 12 EndFraction\"><mi>r</mi><mfenced><mi>m</mi></mfenced><mo>=</mo><mn>90,000</mn><msup><mfenced><mn>1.06</mn></mfenced><mfrac><mi>m</mi><mn>12</mn></mfrac></msup></math>.</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"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=\"r left parenthesis m right parenthesis equals StartFraction 90,000 Over 12 EndFraction left parenthesis 1.06 right parenthesis Superscript m\"><mi>r</mi><mfenced><mi>m</mi></mfenced><mo>=</mo><mfrac><mn>90,000</mn><mn>12</mn></mfrac><msup><mfenced><mn>1.06</mn></mfenced><mi>m</mi></msup></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"r left parenthesis m right parenthesis equals 90,000 left parenthesis StartFraction 1.06 Over 12 EndFraction right parenthesis Superscript m\"><mi>r</mi><mfenced><mi>m</mi></mfenced><mo>=</mo><mn>90,000</mn><msup><mfenced><mfrac><mn>1.06</mn><mn>12</mn></mfrac></mfenced><mi>m</mi></msup></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"r left parenthesis m right parenthesis equals 90,000 left parenthesis StartFraction 1.06 Over 12 EndFraction right parenthesis Superscript StartFraction m Over 12 EndFraction\"><mi>r</mi><mfenced><mi>m</mi></mfenced><mo>=</mo><mn>90,000</mn><msup><mfenced><mfrac><mn>1.06</mn><mn>12</mn></mfrac></mfenced><mfrac><mi>m</mi><mn>12</mn></mfrac></msup></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"r left parenthesis m right parenthesis equals 90,000 left parenthesis 1.06 right parenthesis Superscript StartFraction m Over 12 EndFraction\"><mi>r</mi><mfenced><mi>m</mi></mfenced><mo>=</mo><mn>90,000</mn><msup><mfenced><mn>1.06</mn></mfenced><mfrac><mi>m</mi><mn>12</mn></mfrac></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}}