SAT Math Multiple Choice Question 276: Answer and Explanation

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Question: 276

6. An alloy is a metal made by mixing and melting two or more metals together. After the metals are mixed, the alloy must be cooled slowly to avoid crystallization. Suppose a metallurgist heats a mixture of metals to a temperature of 2,500°F and then removes the resulting alloy from the furnace. The alloy will then cool at a constant rate of 40°F every 15 minutes until it reaches room temperature. Which of the following functions represents the temperature T of the alloy h hours after it was removed from the furnace until it reaches room temperature?

  • A. T(h) = -15h + 2,500
  • B. T(h) = -40h + 2,500
  • C. T(h) = -160h + 2,500
  • D. T(h) = -600h + 2,500

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Passport to Advanced Math / Functions

Strategic Advice: Take a quick peek at the answer choices-but only to get an idea of how the functions look. They are all linear equations, so apply what you know about the slope-intercept form of a line to choose the correct function.

Getting to the Answer: In a real-world scenario, the slope of a line represents a rate of change (how fast the alloy cools) and the y-intercept represents a starting amount (the initial temperature of the alloy). Be careful-the rate is given in minutes while the question asks for a function in terms of hours. There are four 15-minute intervals in an hour, so the cooling rate per hour is -40(4) = -160 degrees. (The rate is negative because as the alloy cools, the temperature drops.) Look back at the answer choices-(C) is the only one that has a slope of -160, so (C) is correct.

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