Question #59d1f4b5 - SAT Suite Question Bank

ID: 59d1f4b5

Modded SAT Question Bank by Abdullah Mallik

$M equals 1,800 times, 1 point 0 2, to the power t$

The equation above models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years after the gym opens?

$M equals 1,800 times, 1 point 0 2, to the power of the fraction q over 4$
$M equals 1,800 times, 1 point 0 2, to the power 4 q$
$M equals 1,800 times, 1 point 0 0 5, to the power 4 q$
$M equals 1,800 times, 1 point 0 8 2, to the power q$

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Correct Answer: A

Rationale

Choice A is correct. In 1 year, there are 4 quarter years, so the number of quarter years, q, is 4 times the number of years, t ; that is, $q, equals 4, t$ . This is equivalent to $t equals, q over 4$ , and substituting this into the expression for M in terms of t gives $M equals, 1,800 times, 1 point 0 2 raised to the fraction q over 4 power$ .

Choices B and D are incorrect and may be the result of incorrectly using $t equals, 4 q$ instead of $q, equals 4, t$ . (Choices B and D are nearly the same since $1 point 0 2 raised to the 4 q power$ is equivalent to $open parenthesis, 1 point 0 2 to the fourth power, close parenthesis, raised to the q power$ , which is approximately $1 point 0 8 2 to the q power$ .) Choice C is incorrect and may be the result of incorrectly using $t equals, 4 q$ and unnecessarily dividing 0.02 by 4.

Question Difficulty: Hard