{"id":"cb_question_bank:a1f76398-0aec-4592-821b-537775e3d775","source_id":"cb_question_bank","source_item_id":"a1f76398-0aec-4592-821b-537775e3d775","external_id":"d1baa89a-a42c-46e1-a485-7574f59a8753","ibn":null,"question_id":"7ba694f3","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The number of bacteria in a liquid medium doubles every day. There are 44,000 bacteria in the liquid medium at the start of an observation. Which represents the number of bacteria, y , in the liquid medium t days after the start of the observation?","stimulus":"","stimulus_html":null,"stem_html":"<p>The number of bacteria in a liquid medium doubles every day. There are <math alttext=\"44,000\"><mn>44,000</mn>\n</math> bacteria in the liquid medium at the start of an observation. Which represents the number of bacteria, <math alttext=\"y\"><mi>y</mi>\n</math>, in the liquid medium <math alttext=\"t\"><mi>t</mi>\n</math><em>&nbsp;</em>days after the start of the observation?&nbsp;</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. Since the number of bacteria doubles every day, the relationship between <math alttext=\"t\"><mi>t</mi>\n</math> and <math alttext=\"y\"><mi>y</mi>\n</math> can be represented by an exponential equation of the form <math alttext=\"y equals a left parenthesis b right parenthesis Superscript t\"><mi>y</mi><mo>=</mo><mi>a</mi><msup><mfenced><mi>b</mi></mfenced><mi>t</mi></msup></math>, where <math alttext=\"a\"><mi>a</mi>\n</math> is the number of bacteria at the start of the observation and the number of bacteria increases by a factor of <math alttext=\"b\"><mi>b</mi>\n</math> every day. It’s given that there are <math alttext=\"44,000\"><mn>44,000</mn>\n</math> bacteria at the start of the observation. Therefore, <math alttext=\"a equals 44,000\"><mrow>\n\t<mi>a</mi>\n\t<mo>=</mo>\n\t<mn>44,000</mn>\n</mrow>\n</math>. It’s also given that the number of bacteria doubles, or increases by a factor of <math alttext=\"2\"><mn>2</mn>\n</math>, every day. Therefore, <math alttext=\"b equals 2\"><mrow>\n\t<mi>b</mi>\n\t<mo>=</mo>\n\t<mn>2</mn>\n</mrow>\n</math>. Substituting <math alttext=\"44,000\"><mn>44,000</mn>\n</math> for <math alttext=\"a\"><mi>a</mi>\n</math> and <math alttext=\"2\"><mn>2</mn>\n</math> for <math alttext=\"b\"><mi>b</mi>\n</math> in the equation <math alttext=\"y equals a left parenthesis b right parenthesis Superscript t\"><mi>y</mi><mo>=</mo><mi>a</mi><msup><mfenced><mi>b</mi></mfenced><mi>t</mi></msup></math>&nbsp;yields <math alttext=\"y equals 44,000 left parenthesis 2 right parenthesis Superscript t\"><mi>y</mi><mo>=</mo><mn>44,000</mn><msup><mfenced><mn>2</mn></mfenced><mi>t</mi></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. This equation represents a situation where the number of bacteria is decreasing by half, not doubling, every day.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.825000+00:00","source_updated_at":"2023-08-02T20:25:59.825000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"y equals one half left parenthesis 44,000 right parenthesis Superscript t\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mfenced><mrow><mn>44,000</mn></mrow></mfenced><mi>t</mi></msup></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"y equals 2 left parenthesis 44,000 right parenthesis Superscript t\"><mi>y</mi><mo>=</mo><mn>2</mn><msup><mfenced><mrow><mn>44,000</mn></mrow></mfenced><mi>t</mi></msup></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"y equals 44,000 left parenthesis one half right parenthesis Superscript t\"><mi>y</mi><mo>=</mo><mrow><mn>44,000</mn></mrow><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mi>t</mi></msup></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"y equals 44,000 left parenthesis 2 right parenthesis Superscript t\"><mi>y</mi><mo>=</mo><mrow><mn>44,000</mn></mrow><msup><mfenced><mn>2</mn></mfenced><mi>t</mi></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}}