PSAT Math Multiple-Choice Practice Question 168

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).