PSAT Math Multiple-Choice Question 67: Answer and Explanation

Question: 67

T(t) = ΔT^(-kt)

The simple cooling of an object can be represented by the equation above, where T is temperature in degrees Celsius, k is a rate constant, and t is time. What might the quantity ΔT represent?

• A. Temperature at a certain time
• B. The difference between the initial temperature of the object and the temperature of its surroundings
• C. A conversion from Celsius to Fahrenheit
• D. A constant factor that is dependent on the object

Correct Answer: B

Explanation:

B

The question asks for the meaning of a quantity in context. Start by reading the full question, which asks for the meaning of the quantity ΔT. Then label the parts of the equation with the information given. The question states that the equation represents the cooling of an object over time. According to the question, T is temperature in degrees Celsius, k is a rate constant, and t is time. Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) refers to temperature, T, but it also includes time, t, so eliminate (A). Choice (B) refers to a difference between the temperature of the object and the temperature of its surroundings, so keep (B). Eliminate (C) because the question does not mention Fahrenheit. Eliminate (D) because it mentions a constant factor, which corresponds with the constant rate, k. By Process of Elimination, only (B) remains. Though it is not necessary to know this to answer the question, the symbol Δ (called "delta") is used to represent a change or difference. The correct answer is (B).