{"id":"cb_question_bank:b3f85b4c-d189-45d0-a8f4-8a4a523c50d1","source_id":"cb_question_bank","source_item_id":"b3f85b4c-d189-45d0-a8f4-8a4a523c50d1","external_id":"b43f007e-8a7c-48b8-8a0a-eeb0f65e3faf","ibn":null,"question_id":"c048055c","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A model predicts that the population of Springfield was 15,000 in 2005 . The model also predicts that each year for the next 5 years, the population p increased by 4 percent sign of the previous year's population. Which equation best represents this model, where x is the number of years after 2005 , for x less than or equals 5 ?","stimulus":"","stimulus_html":null,"stem_html":"

A model predicts that the population of Springfield was 15,000\n in 2005. The model also predicts that each year for the next 5\n years, the population p\n increased by 4% of the previous year's population. Which equation best represents this model, where x\n is the number of years after 2005, for x≤5?

","rationale_html":"

Choice D is correct. It's given that a model predicts the population of Springfield in 2005 was 15,000\n. The model also predicts that each year for the next 5\n years, the population increased by 4% of the previous year's population. The predicted population in one of these years can be found by multiplying the predicted population from the previous year by 1.04\n. Since the predicted population in 2005 was 15,000\n, the predicted population 1\n year later is 15,000(1.04). The predicted population 2\n years later is this value times 1.04\n, which is 15,0001.041.04, or 15,0001.042. The predicted population 3\n years later is this value times 1.04\n, or 15,0001.043. More generally, the predicted population, p\n, x\n years after 2005 is represented by the equation p=15,0001.04x. 

\n

Choice A is incorrect. Substituting 0\n for x\n in this equation indicates the predicted population in 2005 was 0.96\n rather than 15,000\n.

\n

Choice B is incorrect. Substituting 0\n for x\n in this equation indicates the predicted population in 2005 was 1.04\n rather than 15,000\n.

\n

Choice C is incorrect. This equation indicates the predicted population is decreasing, rather than increasing, by 4% each year.

","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.825000+00:00","source_updated_at":"2023-08-02T20:25:59.825000+00:00","options":[{"label":"A","content_html":"

p=0.9615,000x

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

p=1.0415,000x

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

p=15,0000.96x

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

p=15,0001.04x

","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}}