{"id":"cb_practice_pdf:t5-math-m2-q25","source_id":"cb_practice_pdf","source_item_id":"t5-math-m2-q25","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-5","module_number":2,"position":25,"stem":"6/4 t P t = 260 1.04 The function P models the population, in thousands, of a certain city t years after 2003. According to the 4% model, the population is predicted to increase by every n months. What is the value of n?","stimulus":"","stimulus_html":null,"stem_html":"<p>6/4 t P t = 260 1.04 The function P models the population, in thousands, of a certain city t years after 2003. According to the 4% model, the population is predicted to increase by every n months. What is the value of n?</p>","rationale_html":"<p>Choice A is correct. It’s given that the function P models the population, in 2003 thousands, of a certain city t years after . The value of the base of the given 1.04 4% exponential function, , corresponds to an increase of for every increase 6 6 =0 of 1 in the exponent, b4lt. If the exponent is equal to 0, then b4lt . Multiplying 4 = both sides of this equation by b6l yields t 0. If the exponent is equal to 1, then 6 =1 4 =4 =2 b4lt . Multiplying both sides of this equation by b6l yields t 6, or t 3. 4% 2 Therefore, the population is predicted to increase by every 3 of a year. It’s 4% given that the population is predicted to increase by every n months. Since 12 2 2 12 there are months in a year, 3 of a year is equivalent to b3l` j, or 8, months. Therefore, the value of n is 8. Choice B is incorrect. This is the number of months in which the population is 4% =260 1.04 t predicted to increase by according to the model P^th ^ h, not 6 P^th =260 ^ 1.04 h c4mt . Choice C is incorrect. This is the number of months in which 4% the population is predicted to increase by according to the model 4 6 P^th =260 ^ 1.04 h c6mt , not P^th =260 ^ 1.04 h c4mt . Choice D is incorrect. This is the number of months in which the population is predicted to increase by 1 6 4% according to the model P^th =260 ^ 1.04 h c6mt , not P^th =260 ^ 1.04 h c4mt .</p>","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>8</p>","ord":0},{"label":"B","content_html":"<p>12</p>","ord":1},{"label":"C","content_html":"<p>18</p>","ord":2},{"label":"D","content_html":"<p>72</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}}