ID: 59d1f4b5
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)
Comment: Apply the KISS principle (Keep It Simple, Stupid).
Method 1: There are 4 quarters in a year, so when q = 4, the result of the function should be identical to when t = 1. Eyeball the answer choices. If 1 year proves too simple, as in multiple answers would work, try 2 years (8 quarters).
M = 1,800(1.02)^t
M = 1,800(1.02)^1
M = 1,800(1.02)
A. M = 1,800(1.02)^((4)/4) --> M = 1,800(1.02)^1 --> M = 1,800(1.02) √
B. M = 1,800(1.02)^(4(4)) --> M = 1,800(1.02)^16 X
C. M = 1,800(1.005)^(4(4)) --> M = 1,800(1.005)^16 X
D. M = 1,800(1.082)^(4) --> M = 1,800(1.082)^4 X
With three answers that do not work and one that does, it is clear that the correct answer is (A).
Method 2: Apart from possibly using the calculator to work through any arithmetic you would choose to do, there is no need to use one. A graph would not really be helpful without understanding the relationship between 4 quarters of a year and 1 year.
Method 3: Conceptually, there is a 2 percent growth in membership per year, so the correct answer would have to model the same growth per year, just broken down into quarters.
A. This would represent a 2 percent growth in membership over 4 quarters, or 1 year. √
B. This would represent a 2 percent growth, but not per quarter. The variable q would have to be 1/4 to align the two models, and 1/4 of a quarter is not the same as 1 year. X
C. This would represent a 0.5 percent growth, and again, not per quarter, but per 1/4 of a quarter. This is a complete mess. X
D. This would represent an 8.2 percent growth per quarter, clearly overshooting the target. X
The correct answer is (A).
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