{"id":"cb_question_bank:25957940-be96-409d-8aaf-fff875e2189e","source_id":"cb_question_bank","source_item_id":"25957940-be96-409d-8aaf-fff875e2189e","external_id":null,"ibn":"08160-DC","question_id":"263f9937","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":"A culture of bacteria is growing at an exponential rate, as shown in the table above. At this rate, on which day would the number of bacteria per milliliter reach 5 point 1 2, times 10, to the power 8 ?","stimulus":"Growth of a Culture of Bacteria Day Number of bacteria per milliliter at end of day 1 2 point 5 times 10 to the power 5 2 5 point 0 times 10 to the power 5 3 1 point 0 times 10 to the power 6","stimulus_html":"
\n
\n
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\n \n \n \n \n \n \n \n \n \n
Growth of a Culture of Bacteria
DayNumber of bacteria per
\n\tmilliliter at end of day
1\n \"2
2\n \"5
3\n \"1
\n
\n
\n
\n","stem_html":"

A culture of bacteria is growing at an exponential rate, as shown in the table above. At this rate, on which day would the number of bacteria per milliliter reach \"5?

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Choice D is correct. The number of bacteria per milliliter is doubling each day. For example, from day 1 to day 2, the number of bacteria increased from 2.5 × 105 to 5.0 × 105. At the end of day 3 there are 106 bacteria per milliliter. At the end of day 4, there will be 106 × 2 bacteria per milliliter. At the end of day 5, there will be (106 × 2) × 2, or 106 × (22) bacteria per milliliter, and so on. At the end of day d, the number of bacteria will be 106 × (2d – 3). If the number of bacteria per milliliter will reach 5.12 × 108 at the end of day d, then the equation \"10 must hold. Since 5.12 × 108 can be rewritten as 512 × 106,  the equation is equivalent to \"2. Rewriting 512 as 29 gives d – 3 = 9, so d = 12. The number of bacteria per milliliter would reach 5.12 × 108 at the end of day 12.

Choices A, B, and C are incorrect. Given the growth rate of the bacteria, the number of bacteria will not reach 5.12 × 108 per milliliter by the end of any of these days.

\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.635000+00:00","source_updated_at":"2023-08-02T20:25:59.635000+00:00","options":[{"label":"A","content_html":"

Day 5

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Day 9

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Day 11

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Day 12

\n","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}}