Question

Bacteria such as V. cholerae are known to follow an exponential growth curve rate, and will double their number every 15 minutes. Fortunately, anti-bacterial hand wash can kill 99.9% of bacteria on a surface. If a colony of 500 V. cholerae cells are left alone for 2 hours, then anti-bacterial handwash is applied thoroughly, how many bacterial cells are left?

A. 4 cells
B. 64 cells
C. 128 cells
D. 256 cells
E. 512 cells

Answer 1

After 2 hours of exponential growth, a colony of 500 V. cholerae cells increases to 64,000 cells. Upon using an anti-bacterial hand wash that kills 99.9% of the bacteria, 64 cells remain.

Step-by-step explanation:

Bacteria such as V. cholerae experience exponential growth and the colony will double every 15 minutes. To calculate the number of bacteria after 2 hours, we need to determine how many 15-minute intervals are in 2 hours. There are 8 such intervals in 2 hours (120 minutes / 15 minutes per interval). If we start with 500 bacteria, after one interval, there will be 500 x 2 = 1,000 bacteria. Continuing this process eight times: 1,000(2nd interval) -> 2,000(3rd interval) -> 4,000(4th interval) -> 8,000(5th interval) -> 16,000(6th interval) -> 32,000(7th interval) -> 64,000(8th interval).

After 2 hours, we would have 64,000 bacteria. Applying an anti-bacterial hand wash that kills 99.9% of the bacteria, the number of bacteria remaining is 0.1% of 64,000: 64,000 x 0.001 = 64 bacteria. To calculate the number of bacterial cells left after 2 hours, we need to divide the total time by the doubling time to find the number of generations. Since the doubling time is 15 minutes, there are 2 x 60 / 15 = 8 generations in 2 hours. Each generation doubles the number of cells, so the final number of cells is 500 x (2^8) = 500 x 256 = 128,000 cells.