{"id":"cb_practice_pdf:t8-math-m2-q27","source_id":"cb_practice_pdf","source_item_id":"t8-math-m2-q27","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":"spr","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-8","module_number":2,"position":27,"stem":"The quadratic function g models the depth, in meters, below the surface of the water of a seal t minutes after the seal entered the water during a dive. The function estimates that the seal reached its maximum depth of 302.4 meters 6 minutes after it entered the water and then reached the surface of the water 12 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 10 minutes after it entered the water? OP","stimulus":"","stimulus_html":null,"stem_html":"<p>The quadratic function g models the depth, in meters, below the surface of the water of a seal t minutes after the seal entered the water during a dive. The function estimates that the seal reached its maximum depth of 302.4 meters 6 minutes after it entered the water and then reached the surface of the water 12 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 10 minutes after it entered the water? OP</p>","rationale_html":"<p>168 The correct answer is . The quadratic function g gives the estimated depth of the seal, g^th, in meters, t minutes after the seal enters the water. It’s given that 302.4 function g estimates that the seal reached its maximum depth of meters 6 minutes after it entered the water. Therefore, function g can be expressed in = -6 2+302.4 vertex form as g^th a^t h , where a is a constant. Since it’s also given 12 12 =0 that the seal reached the surface of the water after minutes, g^ h . 12 = -6 2+302.4 Substituting for t and 0 for g^th in g^th a^t h yields 0= 12-6 2+302.4 36 =-302.4 36 a^ h , or a . Dividing both sides of this equation by =-8.4 -8.4 = -6 2+302.4 gives a . Substituting for a in g^th a^t h gives =-8.4 -6 2+302.4 10 g^th ^t h . Substituting for t in g^th gives 10 =-8.4 10-6 2+302.4 10 =-8.4 4 2+302.4 g^ h ^ h , which is equivalent to g^ h ^ h , or 10 =168 g^ h . Therefore, the estimated depth, to the nearest meter, of the seal 10 168 minutes after it entered the water was meters. 48 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS</p>","correct_answer":["168"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"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}}