{"id":"cb_question_bank:b42df7c5-471b-47c1-ab3c-9bd8bfdf3c8d","source_id":"cb_question_bank","source_item_id":"b42df7c5-471b-47c1-ab3c-9bd8bfdf3c8d","external_id":null,"ibn":"025702-DC","question_id":"70ebd3d0","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function N defined above can be used to model the number of species of brachiopods at various ocean depths d , where d is in hundreds of meters. Which of the following does the model predict?","stimulus":"N of d, equals, 115 times, open parenthesis, 0.90, close parenthesis, raised to the d power.","stimulus_html":"
\n\t

\"N

\n
\n","stem_html":"

The function N defined above can be used to model the number of species of brachiopods at various ocean depths d, where d is in hundreds of meters. Which of the following does the model predict?

\n","rationale_html":"

Choice D is correct. The function N is exponential, so it follows that \"N changes by a fixed percentage for each increase in d by 1. Since d is measured in hundreds of meters, it also follows that the number of brachiopod species changes by a fixed percentage for each increase in ocean depth by 100 meters. Since the base of the exponent in the model is 0.90, which is less than 1, the number of brachiopod species decreases as the ocean depth increases. Specifically, the number of brachiopod species at a depth of \"d meters is 90% of the number of brachiopod species at a depth of d meters. This means that for each increase in ocean depth by 100 meters, the number of brachiopod species decreases by 10%.

Choices A and C are incorrect. These describe situations where the number of brachiopod species are decreasing linearly rather than exponentially. Choice B is incorrect and results from interpreting the decrease in the number of brachiopod species as 10% for every 1-meter increase in ocean depth rather than for every 100-meter increase in ocean depth.

 

\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+00:00","options":[{"label":"A","content_html":"

For every increase in depth by 1 meter, the number of brachiopod species decreases by 115.

\n","ord":0},{"label":"B","content_html":"

For every increase in depth by 1 meter, the number of brachiopod species decreases by 10%.

\n","ord":1},{"label":"C","content_html":"

For every increase in depth by 100 meters, the number of brachiopod species decreases by 115.

\n","ord":2},{"label":"D","content_html":"

For every increase in depth by 100 meters, the number of brachiopod species decreases by 10%.

\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}}