PSAT Math Multiple-Choice Question 168: Answer and Explanation

Question: 168

The amount of carbon-14 in a sample halves every 5,730 years. Which of the following best describes the type of decay that models the relationship between amount of carbon-14 and time?

• A. Linear decay, because the amount of carbon-14 decreases by the same factor every 5,730-year period
• B. Linear decay, because the amount of carbon-14 decreases by the same amount every 5,730-year period
• C. Exponential decay, because the amount of carbon-14 decreases by the same factor every 5,730-year period
• D. Exponential decay, because the amount of carbon-14 decreases by the same amount every 5,730-year period

Correct Answer: C

Explanation:

C

The question asks for the model that best describes the decay of the amount of carbon-14 over time. Compare the answer choices. Two of the choices describe linear decay and two describe exponential decay. Linear decay describes a relationship in which the decrease is by a constant amount. Exponential decay describes a relationship in which the decrease is by a constant factor or percent. Eliminate (A) and (D), which reverse the definitions. According to the question, the amount of carbon-14 halves every 5,730 years. This is a reduction by the same factor. To better see this, plug in. If there are 100 grams of carbon-14 to start, then in 5,730 years, there will be 50 grams. In another 5,730 years, there will be 25 grams. Since the amount of the decrease was not constant, eliminate (B). The correct answer is (C).