{"id":"cb_practice_pdf:t10-math-m1-q16","source_id":"cb_practice_pdf","source_item_id":"t10-math-m1-q16","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-10","module_number":1,"position":16,"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 of the following 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 44,000 bacteria in the liquid medium at the start of an observation. Which of the following represents the number of bacteria, y, in the liquid medium t days after the start of the observation?</p>","rationale_html":"<p>Choice D is correct. Since the number of bacteria doubles every day, the relationship between t and y can be represented by an exponential equation of = t the form y a^bh, where a is the number of bacteria at the start of the observation and the number of bacteria increases by a factor of b every day. It’s 44,000 given that there are bacteria at the start of the observation. Therefore, =44,000 a . It’s also given that the number of bacteria doubles, or increases by a = 44,000 factor of 2, every day. Therefore, b 2. Substituting for a and 2 for b in = t =44,000 2 t the equation y a^bh yields y ^ h. 35 SAT PRACTICE TEST #10 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. 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":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>y = 1/2 ( 44,000^t )</p>","ord":0},{"label":"B","content_html":"<p>y = 2 ( 44,000^t ) t   y = 44,000  </p>","ord":1},{"label":"C","content_html":"<p>  1/2    = 44,000 2^t</p>","ord":2},{"label":"D","content_html":"<p>y ( )</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}