{"id":"cb_practice_pdf:t10-math-m1-q17","source_id":"cb_practice_pdf","source_item_id":"t10-math-m1-q17","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":"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-10","module_number":1,"position":17,"stem":"x h(x) 0 1.23 2 1.54 4 1.94 The table shows the exponential relationship between the number of years, x, since Hana started training in pole vault, and the estimated height h(x), in meters, of her best pole vault for that year. Which of the following functions best represents this relationship, where x ≤ 4? () = 1.12 ( 0.23)^x","stimulus":"","stimulus_html":null,"stem_html":"<p>x h(x) 0 1.23 2 1.54 4 1.94 The table shows the exponential relationship between the number of years, x, since Hana started training in pole vault, and the estimated height h(x), in meters, of her best pole vault for that year. Which of the following functions best represents this relationship, where x ≤ 4? () = 1.12 ( 0.23)^x</p>","rationale_html":"<p>Choice D is correct. The table shows an increasing exponential relationship between the number of years, x, since Hana started training in pole vault and the estimated height h^xh, in meters, of her best pole vault for that year. The = x relationship can be written as h^xh Ca , where C and a are positive constants. = =1.23 1.23 It’s given that when x 0, h^xh . Substituting 0 for x and for h^xh in = x 1.23= 0 1.23= 1.23 = x h^xh Ca yields Ca , or C. Substituting for C in h^xh Ca =1.23 x = =1.54 yields h^xh a . It’s also given that when x 2, h^xh . Substituting 2 for 1.54 =1.23 x 1.54=1.23 2 x and for h^xh in h^xh a yields a . Dividing each side of this equation by 1.23 yields 1 1 . . 2 5 3 4 = 1 1 .2 .2 3 3a 2 , or a 2 is approximately equal to 1.252 . 1.252 1.12 1.12 Since a is positive, a is approximately equal to , or . Substituting =1.23 x =1.23 1.12 x for a in h^xh a yields h^xh ^ h . = Choice A is incorrect. When x 0, the value of h^xh in this function is equal to 1.12 1.23 rather than , and it is decreasing rather than increasing. Choice B is = 1.12 incorrect. When x 0, the value of h^xh in this function is equal to rather 1.23 than . Choice C is incorrect. This function is decreasing rather than increasing.</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>h x = 1.12 1.23</p>","ord":0},{"label":"B","content_html":"<p>h ( x ) ( )^x = 1.23 0.12</p>","ord":1},{"label":"C","content_html":"<p>h ( x ) ( )^x = 1.23 1.12</p>","ord":2},{"label":"D","content_html":"<p>h ( x ) ( )^x</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}}