PSAT Math Multiple-Choice Question 138: Answer and Explanation

Question: 138

The membership of a sports fan group increases by 10 percent each month during the season. What type of relationship exists between the size of the fan group and the number of months since the start of the season?

• A. Exponential relationship in which higher membership numbers correspond to earlier dates in the season
• B. Linear relationship whose graph has a slope greater than 0
• C. Exponential relationship in which higher membership numbers correspond to later dates in the season
• D. Linear relationship whose graph has a slope less than 0

Correct Answer: C

Explanation:

C

The question asks for the relationship between two variables. If the fan group increases by a certain percentage each month, then the actual number of additional members each month increases as the size of the group increases. This is exponential growth, so eliminate (B) and (D), which indicate linear growth. Compare the remaining answer choices. The difference between (A) and (C) is when the higher numbers will occur. Because the size of the group is increasing, later dates will have higher membership numbers; eliminate (A). The correct answer is (C).