{"id":"cb_question_bank:89ce4f50-a72a-4148-890b-04f0f0723185","source_id":"cb_question_bank","source_item_id":"89ce4f50-a72a-4148-890b-04f0f0723185","external_id":"dbd2580c-f8fe-48de-b7f0-838c5fe91f7c","ibn":null,"question_id":"dd8ac009","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":"Time (years) Total amount (dollars) 0 670.00 1 674.02 2 678.06 Sara opened a savings account at a bank. The table shows the exponential relationship between the time t , in years, since Sara opened the account and the total amount d , in dollars, in the account. If Sara made no additional deposits or withdrawals, which of the following equations best represents the relationship between t and d ?","stimulus":"","stimulus_html":null,"stem_html":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Time (years)Total amount (dollars)
0670.00
1674.02
2678.06
\n

Sara opened a savings account at a bank. The table shows the exponential relationship between the time t\n, in years, since Sara opened the account and the total amount d\n, in dollars, in the account. If Sara made no additional deposits or withdrawals, which of the following equations best represents the relationship between t\n and d\n?

","rationale_html":"

Choice B is correct. It’s given that the relationship between t\n and d\n is exponential. The table shows that the value of d\n increases as the value of t\n increases. Therefore, the relationship between t\n and d\n can be represented by an increasing exponential equation of the form d=a1+bt, where a\n and b\n are positive constants. The table shows that when \n\tt\n\t=\n\t0\n\n, \n\td\n\t=\n\t670\n\n. Substituting 0\n for t\n and 670\n for d\n in the equation d=a1+bt yields 670=a1+b0, which is equivalent to 670=a1, or 670=a. Substituting 670\n for a\n in the equation d=a1+bt yields d=6701+bt. The table also shows that when \n\tt\n\t=\n\t1\n\n, \n\td\n\t=\n\t674.02\n\n. Substituting 1\n for t\n and 674.02\n for d\n in the equation d=6701+bt yields 674.02=6701+b1, or 674.02=6701+b. Dividing both sides of this equation by 670\n yields 1.006=1+b. Subtracting 1\n from both sides of this equation yields \n\tb\n\t=\n\t0.006\n\n. Substituting 0.006\n for b\n in the equation d=6701+bt yields d=6701+0.006t. Therefore, of the choices, choice B best represents the relationship between t\n and d\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":true,"source_created_at":"2023-08-02T20:25:59.828000+00:00","source_updated_at":"2023-08-02T20:25:59.828000+00:00","options":[{"label":"A","content_html":"

d=0.0061+670t

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

d=6701+0.006t

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

d=1+0.006t

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

d=1+670t

","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}}