What is the doubling time in minutes of a bacterial population that went from 100 to 100,000 cells in 5 hours?

Question

A slant is inoculated with 100 E. Coli cells. The slant is left at room temperature where the generation time is 1 hour. How many E. Coli are in the slant in 6 hours? If the slant was initially put in the 37 C incubator with a 20 min generation time how many more cells would have grown in the same time peroid

Answer 1

100 * 2^x = 100000

2^x = 100000 / 100 = 1000

x log 2 = log 1000 = 3

x = 3 / log 2 = 9.9658

5 hours = 300 minutes

300 / 9.9658 = 30.1 minutes

Note that 2^10 = 1024, so the exponent needs to be a little less than 10.