{"id":"cb_practice_pdf:t4-math-m2-q23","source_id":"cb_practice_pdf","source_item_id":"t4-math-m2-q23","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-4","module_number":2,"position":23,"stem":"- f(x) 5,470(0.64)^x 12 = The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p%of its value the preceding year, what is the value of p?","stimulus":"","stimulus_html":null,"stem_html":"<p>- f(x) 5,470(0.64)^x 12 = The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p%of its value the preceding year, what is the value of p?</p>","rationale_html":"<p>( )= ( )x Choice C is correct. For a function of the form f x a r k, where a, r, and k are &lt; ( ) ( - ) constants and r 1, the value of f x decreases by 100 1 r % for every = = = increase of x by k. In the given function, a 5,470, r 0.64, and k 12. ( ) ( - ) Therefore, for the given function, the value of f x decreases by 100 1 0.64 %, ( ) or 36%, for every increase of x by 12. Since f x represents the value, in dollars, of the equipment after x months of use, it follows that the value of the equipment decreases every 12 months by 36% of its value the preceding 12 months. Since there are 12 months in a year, the value of the equipment decreases each year by 36% of its value the preceding year. Thus, the value of p is 36. 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 D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>4</p>","ord":0},{"label":"B","content_html":"<p>5</p>","ord":1},{"label":"C","content_html":"<p>36</p>","ord":2},{"label":"D","content_html":"<p>64</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}}