SAT Math Multiple Choice Question 531: Answer and Explanation

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Question: 531


If an exponential function is used to model the data shown in the figure, and it is written in the form f(x) = f(0)(1 + r)x, what would be the value of r?

  • A. 2
  • B. 3
  • C. 4
  • D. 5

Correct Answer: B



Difficulty: Medium

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: When an exponential function is written in the form f(x) = f(0)(1 + r)x, the quantity (1 + r) represents the growth rate or the decay rate depending on whether the y-values are increasing or decreasing.

Getting to the Answer: The y-values are increasing in this graph, so r represents a growth rate. Because the data is modeled using an exponential function (not a linear function), the rate is not the same as the slope. Look at the y-values in the calculator screenshot—they are quadrupling as the x-values increase by 1. In the equation, this means that (1 + r) = 4. Solve this equation to find that r = 3.

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