# Math Club Problem of the Month

As you may know, CPSD pool-tested approximately 3500 students before returning to school. Students were put in pools of 10; each pool was tested once, and for every pool that tested positive, each student in the pool was tested individually to determine which students had COVID-19. Due to complications at the lab, most students did not receive their results, but the testing process could have been carried out more efficiently with a different pool size. We can assume that the positivity rate was about 6%, similar to that of Cambridge as of mid-January.

1. (a)  To minimize the total number of tests performed, should the pool size be increased or decreased?
2. (b)  Find the pool size that minimizes the number of tests performed. (Hint: First, express the number of tests in terms of the pool size; then graph this function to find the minimum.)
3. (c)  With a sufficiently high positivity rate, it would be more efficient to opt for individual testing rather than pool testing. Find the percent positivity at which this occurs.

Come to Math Club at 3 PM on Wednesday, February 9, in Room 3607 to discuss this problem!