PSAT Math Multiple-Choice Question 425: Answer and Explanation

Question: 425

An environmental agency is working to reduce the amount of toxic waste that a company discards in the ocean. Currently, the company discards 10.8 -million pounds of toxic waste annually, and the agency's goal is to eliminate that amount by collecting the toxic waste and putting it through a process that makes the substance nontoxic. If the agency increases its processing capacity at a constant rate and meets its goal at the end of the 14th year, which of the following linear functions f could the agency use to model the amount of toxic waste (in millions of pounds) being added to the ocean t years into the -program?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Describing Real-Life Situations with Functions

Strategic Advice: When modeling a real-life situation with a linear function, the starting point in the description is the y-intercept of the equation and the rate of change is the slope. Eliminate choices as you go; you may find that you are able to answer the question after only one or two steps. Never do more math than necessary to answer the question.

Getting to the Answer: In this question, the agency is reducing the amount of toxic waste disposed annually, so the slope must be negative. Eliminate (C) and (D) because their positive slopes indicate an increasing function.

The starting point, or y-intercept, is the amount of toxic waste the company is now discarding, or 10.8 million pounds. Unfortunately, this value is the same in (A) and (B), so you'll need to calculate the value of the slope more precisely.

The agency wants to eliminate all toxic waste produced in a year by the end of 14 years, so to find the amount of reduction per year, divide 10.8 by 14.

The value does not appear in the choices, and the slopes in the choices do not have decimal points, so multiply the fraction by 1 in the form of and reduce until you see a value that matches an answer choice. So, so (B) is correct.