SAT Math Multiple Choice Question 468: Answer and Explanation

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Question: 468

3.

The calculator screenshot above shows the x- and y-values for the first few data points shown in the scatterplot, which can be modeled using an exponential function. Which of the following scenarios could be represented by this function?

  • A. The resale value of a car is cut in half for every 3,600 miles driven.
  • B. The resale value of a car decreases by $5,000 for every 3,600 miles driven.
  • C. The resale value of a car decreases by $3,600 for every 5,000 miles driven.
  • D. The resale value of a car decreases by approximately 12% for every 5,000 miles driven.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: You are told that the function is exponential, which means the y-values are not changing by a constant amount (which is supported by the values in the calculator screenshot).

Getting to the Answer: You can immediately eliminate B and C because these describe linear functions (the value decreases by a constant amount each time). To choose between A and (D), think logically about how the graph would be labeled (if it had labels). The value of a car depends on how many miles it has been driven, so value would be plotted along the y-axis, and miles driven would be plotted along the x-axis. Now, apply this to the values in the calculator screenshot. The miles driven (x) increase by 5,000 each time, and for every 5,000-mile increase, the value of the car drops. This means (D) is correct. To check this answer, you can multiply each y-value in the table by 100 – 12 = 88%, or 0.88, to see if the values are in fact decreasing by 12% each time (which they are).

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