A company opens an account with an initial balance $36,100.00 of. The account earns interest, and no additional deposits or withdrawals are made. The account balance is given by an exponential A(t) function A, where is the account balance, in dollars, t years after the account is opened. The $68,071.93 account balance after 13 years is. Which equation could define A? A t = 36,100.00 1.05^t
","rationale_html":"Choice A is correct. Since it’s given that the account balance, A^th, in dollars, after t years can be modeled by an exponential function, it follows that function A = t can be written in the form A^th Nr, where N is the initial value of the function and r is a constant related to the growth of the function. It’s given that the initial $36,100.00 balance of the account is , so it follows that the initial value of the 36,100.00 36,100.00 function, or N, must be . Substituting for N in the equation = t =36,100.00 t A^th Nr yields A^th r. It’s given that the account balance after 13 =13 $68,071.93 13 =68,071.93 years, or when t , is . It follows that A^ h , 36,100.00 13=68,071.93 or r . Dividing each side of the equation 36,100.00 13=68,071.93 36,100.00 13= 68,071.93 r by yields r 36,100.00. Taking the 13 =13 68,071.93 th root of both sides of this equation yields r 36,100.00, or r is 1.05 1.05 approximately equal to . Substituting for r in the equation =36,100.00 t =36,100.00 1.05 t A^th r yields A^th ^ h, so the equation =36,100.00 1.05 t A^th ^ h could define A. 33 SAT PRACTICE TEST #9 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 Choice B is incorrect. Substituting 0 for t in this function indicates an initial $31,971.93 $36,100.00 balance of , rather than . Choice C is incorrect. Substituting $31,971.93 0 for t in this function indicates an initial balance of , rather than $36,100.00 . Additionally, this function indicates the account balance is decreasing, rather than increasing, over time. Choice D is incorrect. This function indicates the account balance is decreasing, rather than increasing, over time.
","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":"( ) ( ) A t = 31,971.93 1.05^t
","ord":0},{"label":"B","content_html":"( ) ( ) A t = 31,971.93 0.05^t
","ord":1},{"label":"C","content_html":"( ) ( ) A t = 36,100.00 0.05^t
","ord":2},{"label":"D","content_html":"( ) ( )
","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}}