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Time (years) Total amount (dollars) 0 604.00 1 606.42 2 608.84 Rosa opened a savings account at a bank. The table shows the exponential relationship between the time t, in years, since Rosa opened the account and the total amount n, in dollars, in the account. If Rosa made no additional deposits or withdrawals, which of the following equations best represents the relationship between t and n? t n = (1 +604)
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice C is correct. It’s given that the relationship between t and n is exponential. The table shows that the value of n increases as the value of t increases. Therefore, the relationship between t and n can be represented by an = + t increasing exponential equation of the form n a^1 bh, where a and b are = =604 positive constants. The table shows that when t 0, n . Substituting 0 for t 604 = + t 604= 1+ 0 and for n in the equation n a^1 bh yields a^ bh , which is 604= 1 604= 604 equivalent to a^ h, or a. Substituting for a in the equation = + t =604 1+ t = n a^1 bh yields n ^ bh. The table also shows that when t 1, =606.42 606.42 =604 1+ t n . Substituting 1 for t and for n in the equation n ^ bh 606.42=604 1+ 1 606.42=604 1+ yields ^ bh , or ^ bh. Dividing both sides of this 604 1.004=1+ equation by yields approximately b. Subtracting 1 from both 0.004 sides of this equation yields that the value of b is approximately . 0.004 =604 1+ t Substituting for b in the equation n ^ bh yields =604 1+0.004 t n ^ h. Therefore, of the choices, choice C best represents the relationship between t and n. 42 SAT PRACTICE TEST #9 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 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.
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