measures a cluster of bacteria made up of 40 cells. After 3 hours, the cluster has doubled to 80 cells. After 6 hours, it had doubled to 160 cells. How many bacteria will there be after 2 days?

Answer 1

2 days means 48 hours, which is 16 of 3 -hour periods and in each period the number of the cells is multiplied by 2. So:

The Number of the Cells after 16 periods is 40 (2)^16.

In general:

N = 40 (2) ^(h/3) where h is the number of the hours.