PSAT Math Multiple-Choice Question 227: Answer and Explanation

Question: 227

One function of the Environmental Protection Agency (EPA) is to reduce air pollution. After implementing several pollution reduction programs in a certain city, EPA calculated that the air pollution should decrease by approximately 8 percent each year. What kind of function could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes?

• 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/Functions

Getting to the Answer: Determine whether the change in the amount of pollution is a common difference (linear function) or a common ratio (exponential function), or if it changes direction (quadratic or polynomial function). Each year, the amount of pollution should be 100 - 8 = 92% of the year before. You can write 92% as , which represents a common ratio from one year to the next. This means that the best model is an exponential function, (D), of the form y = a · (0.92)^x.