PSAT Math Multiple-Choice Question 500: Answer and Explanation

Question: 500

Research scientists are testing the effect of a new antibiotic on bacterial growth. They start with a colony of 1,500 bacteria and take counts every 10 minutes for an hour, as shown in the table below.

Bacterial Count Over Time Following Antibiotic Treatment

Minutes (m)	Number of bacteria (b)
10	1,390
20	1,280
30	1,170
40	1,060
50	950
60	840

Which of the following represents the best interpretation of the y-intercept of the line created when these data points are plotted in the xy-plane if minutes, m, are plotted on the x-axis and number of bacteria, b, are plotted on the y-axis?

• A. The number of bacteria at the start of the experiment
• B. The rate at which bacteria is decreasing every 10 minutes
• C. The number of intervals for which the number of bacteria is decreasing
• D. The number of bacteria 60 minutes after the experiment begins

Correct Answer: A

Explanation:

A

The question asks about the interpretation of the line of best fit for a graph. The horizontal axis represents minutes, m, and the vertical axis represents the number of bacteria, b. The resulting graph would have a negative slope since b decreases as m increases. The question asks about the y-intercept, which would occur when m = 0. Therefore, the y-intercept must represent the number of bacteria at the start of the experiment. Only (A) reflects this. The correct answer is (A).