SAT Math Multiple Choice Question 350: Answer and Explanation

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Question: 350

5. An environmental protection group had its members sign a pledge to try to reduce the amount of garbage they throw out by 3% 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 × 1,800t
  • B. y = 1,800 × t0.97
  • C. y = 1,800 × 1.97t
  • D. y = 1,800 × 0.97t

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Passport to Advanced Math / Functions

Strategic Advice: 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.

Getting to the Answer: 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 unknown, so the correct equation is y = 1,800 × (1 - 0.03)t, which simplifies to y = 1,800 × 0.97t.

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