PSAT Math Multiple-Choice Question 45: Answer and Explanation

Question: 45

A forest fire is burning an area of forest that is 10 square miles. An air squad is able to reduce the size of the fire by 7% every 12 hours. If F(t) is the area being burned by the fire, which expression for F(t) represents the area of forest still on fire after t hours?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

The question asks for an expression that represents a specific situation. Use Bite-Sized Pieces to eliminate answer choices. The air squad is decreasing the size of the fire by a certain percent over time, so this question is about exponential decay. When the decay rate is a percent of the total, the decay formula is final amount = (original amount) (1 - rate)^{number of changes}. In this case, F(t) is the final amount, and the question asks for the right side of the formula. The original amount is 10, so eliminate (D) because it does not include 10. The original amount must be multiplied by (1 - rate), so eliminate (A) and (C), which use subtraction instead of multiplication. The only remaining answer is (B), and it matches the decay formula: the rate of 7%, or .07, is subtracted from 1, and this amount is raised to a power of . In this case, t is the number of hours the fire has been burning, and the change happens every 12 hours. To see this, plug in t = 24. In 24 hours, there should be 2 changes, and indeed = 2. The correct answer is (B).