Question

A bacteria population doubles every 3 hours. The initial population is 500 bacteria.



In how many hours will the bacteria population reach more than 1,000,000?




18 hours


27 hours


33 hours


48 hours

Answer 1

Every 3 hours the population doubles, so after n three-hour intervals the population is 500·2^n. We need 500·2^n > 1,000,000, i.e. 2^n > 2000.

2^10 = 1024 (too small), 2^11 = 2048 (>2000). So n = 11 intervals → 11·3 = 33 hours.

Answer: 33 hours.