{"id":"cb_question_bank:c7af64c8-342c-40eb-b7f3-038b5fad4353","source_id":"cb_question_bank","source_item_id":"c7af64c8-342c-40eb-b7f3-038b5fad4353","external_id":"bba90b53-4666-4123-babf-8f8dbe2f8a7f","ibn":null,"question_id":"776cfa7c","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Hana deposited a fixed amount into her bank account each month. The function f left parenthesis t right parenthesis equals 100 plus 25 t gives the amount, in dollars, in Hana's bank account after t monthly deposits. What is the best interpretation of 25 in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p>Hana deposited a fixed amount into her bank account each month. The function&nbsp;<math alttext=\"f left parenthesis t right parenthesis equals 100 plus 25 t\"><mi>f</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>100</mn><mo>+</mo><mn>25</mn><mi>t</mi></math> gives the amount, in dollars, in Hana's bank account after <math alttext=\"t\"><mi>t</mi>\n</math> monthly deposits. What is the best interpretation of <math alttext=\"25\"><mn>25</mn>\n</math> in this context?</p>","rationale_html":"<p>Choice A is correct. It's given that <math alttext=\"t\"><mi>t</mi>\n</math> represents the number of monthly deposits. In the given function&nbsp;<math alttext=\"f left parenthesis t right parenthesis equals 100 plus 25 t\"><mi>f</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>100</mn><mo>+</mo><mn>25</mn><mi>t</mi></math>, the coefficient of <math alttext=\"t\"><mi>t</mi>\n</math> is <math alttext=\"25\"><mn>25</mn>\n</math>. This means that for every increase in the value of <math alttext=\"t\"><mi>t</mi>\n</math> by <math alttext=\"1\"><mn>1</mn>\n</math>, the value of&nbsp;<math alttext=\"f left parenthesis t right parenthesis\"><mi>f</mi><mfenced><mi>t</mi></mfenced></math> increases by <math alttext=\"25\"><mn>25</mn>\n</math>. It follows that with each monthly deposit, the amount in Hana's bank account increased by <math alttext=\"dollar sign 25\"><mo>$</mo><mn>25</mn></math>.</p>\n<p>Choice B is incorrect. Before Hana made any monthly deposits, the amount in her bank account was&nbsp;<math alttext=\"dollar sign 100\"><mo>$</mo><mn>100</mn></math>.&nbsp;</p>\n<p>Choice C is incorrect. After <math alttext=\"1\"><mn>1</mn>\n</math> monthly deposit, the amount in Hana's bank account was <math alttext=\"dollar sign 125\"><mo>$</mo><mn>125</mn></math>.&nbsp;</p>\n<p>Choice D is incorrect and may result from conceptual errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.811000+00:00","source_updated_at":"2023-08-02T20:25:59.811000+00:00","options":[{"label":"A","content_html":"<p>With each monthly deposit, the amount in Hana's bank account increased by <math alttext=\"dollar sign 25\"><mo>$</mo><mn>25</mn></math>.</p>","ord":0},{"label":"B","content_html":"<p>Before Hana made any monthly deposits, the amount in her bank account was&nbsp;<math alttext=\"dollar sign 25\"><mo>$</mo><mn>25</mn></math>.</p>","ord":1},{"label":"C","content_html":"<p>After <math alttext=\"1\"><mn>1</mn>\n</math> monthly deposit, the amount in Hana's bank account was <math alttext=\"dollar sign 25\"><mo>$</mo><mn>25</mn></math>.</p>","ord":2},{"label":"D","content_html":"<p>Hana made a total of <math alttext=\"25\"><mn>25</mn>\n</math> monthly deposits.</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}}