PSAT Math Multiple-Choice Question 199: Answer and Explanation

Question: 199

The figure above represents a click-through rate curve, which shows the relationship between a search result position in a list of Internet search results and the number of people who clicked on advertisements on that result's page. Which of the following regression types would be the best model for this data?

• A. A linear function
• B. A quadratic function
• C. A polynomial function
• D. An exponential function

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Problem Solving and Data Analysis/-Scatterplots

Getting to the Answer: You aren't given much information to go on except the shape of the graph, so you'll need to think about what the shape means. Remember, linear functions increase at a constant rate, exponential functions increase at either an increasing or decreasing rate, gradually at first and then more quickly or vice versa, and quadratics and polynomials reverse direction one or more times. The graph begins by decreasing extremely quickly, but then it almost (but not quite) levels off. Therefore, it can't be linear, and because it doesn't change direction, an exponential function, (D), would be the best model for the data.