SAT Math Multiple Choice Question 197: Answer and Explanation

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Question: 197

2. When a virus breaks out, each infected person can infect multiple new people. In a particularly bad flu outbreak at an elementary school, the number of infected people triples each day in the first school week of January. If 5 people were sick with the flu on Monday, which of the following equations best predicts the number of infected people, I(d), d days after Monday?

  • A. I(d) = 5 × 3d2
  • B. I(d) = 5d3
  • C. I(d) = 5 × 3d
  • D. I(d) = 5 × 9d

Correct Answer: C

Explanation:

C Whenever there are variables in the question and in the answer choices, think Plugging In. Let d = 2. On the first day after Monday, 5 × 3 = 15 people will be infected. On the second day after Monday, 15 × 3 = 45 people will be infected. Therefore, when d = 2, the result is 45. Plug 2 in for d in the answer choices to see which answer equals the target number of 45. Choice (A) becomes 5 × 3(22) = 5 × 12 = 60. This does not match the target number, so eliminate (A). Choice (B) becomes 5 × 23 = 40. Eliminate (B). Choice (C) becomes 5 × 32 = 45. Keep (C), but check the remaining choice just in case. Choice (D) becomes 5 × 9(5) = 225. Eliminate (D), and choose (C).

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