PSAT Math Multiple-Choice Question 186: Answer and Explanation

Question: 186

An environmental protection group had its members sign a pledge to try to reduce the amount of garbage they throw out by 3 percent each year. On the year that the pledge was signed, each person threw out an average of 1,800 pounds of garbage. Which exponential function could be used to model the average amount of garbage each person who signed the pledge should throw out each year after signing the pledge?

• A. y = 0.97 × 1,800 t
• B. y = 1,800 × t^0.97
• C. y = 1,800 × 1.97 t
• D. y = 1,800 × 0.97 t

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Passport to Advanced Math/Functions

Getting to the Answer: Whenever a quantity repeatedly increases or decreases by the same percentage (or fraction) over time, an exponential model can be used to represent the situation. Choice (B) is not an exponential equation, so you can eliminate it right away. The amount of garbage is decreasing, so the scenario represents exponential decay and you can use the form y = a × (1 - r)t, where a is the initial amount, r is the rate of decay, and t is time in years. The initial amount is 1,800, the rate is 3%, or 0.03, and t is an unknown quantity, so the correct equation is y = 1,800 × (1 - 0.03)t, which is equivalent to the equation y = 1,800 × 0.97 t. (D) is correct.