Question #281a4f3b - SAT Suite Question Bank

ID: 281a4f3b

Modded SAT Question Bank by Abdullah Mallik

A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, $f of x$ , and the number of years after 2015, x ?

$f of x equals, 0 point 0 2, times open parenthesis, 3,000, close parenthesis, to the x power$
$f of x equals, 0 point 9 8, times open parenthesis, 3,000, close parenthesis, to the x power$
$f of x equals, 3,000, times open parenthesis, 0 point 0 2, close parenthesis, to the x power$
$f of x equals, 3,000, times open parenthesis, 0 point 9 8, close parenthesis, to the x power,$

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Correct Answer: D

Rationale

Choice D is correct. Because the change in the number of students decreases by the same percentage each year, the relationship between the number of students and the number of years can be modeled with a decreasing exponential function in the form $f of x equals, a, times, open parenthesis, 1 minus r, close parenthesis, to the x power$ , where $f of x$ is the number of students, a is the number of students in 2015, r is the rate of decrease each year, and x is the number of years since 2015. It’s given that 3,000 students were enrolled in 2015 and that the rate of decrease is predicted to be 2%, or 0.02. Substituting these values into the decreasing exponential function yields $f of x equals, 3,000 times, open parenthesis, 1 minus 0 point 0 2, close parenthesis, to the x power$ , which is equivalent to $f of x equals, 3,000 times, open parenthesis, 0 point 9 8, close parenthesis, to the x power$ .

Choices A, B, and C are incorrect and may result from conceptual errors when translating the given information into a decreasing exponential function.

Question Difficulty: Medium