SAT Math Multiple Choice Question 502: Answer and Explanation

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Question: 502

7. A microbiologist is studying the effects of a new antibiotic on a culture of 20,000 bacteria. When the antibiotic is added to the culture, the number of bacteria is reduced by half every hour. What kind of function best models the number of bacteria remaining in the culture after the antibiotic is added?

  • A. A linear function
  • B. A quadratic function
  • C. A polynomial function
  • D. An exponential function

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Problem Solving and Data Analysis / Functions

Strategic Advice: Determine whether the change in the number of bacteria is a common difference (linear function) or a common ratio (exponential function) or if the number of bacteria changes direction (quadratic or polynomial function).

Getting to the Answer: The question tells you that the number of bacteria is reduced by half every hour after the antibiotic is applied. The microbiologist started with 20,000, so after one hour, there are 10,000 left, or . After 2 hours, there are 5,000 left, or , and so on. The change in the number of bacteria is a common ratio , so the best model is an exponential function of the form . In this scenario, a is 20,000.

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