Calculation of Generation Time

When growing exponentially by binary fission, the increase in a bacterial population is by geometric progression. If we start with one cell, when it divides, there are 2 cells in the first generation, 4 cells in the second generation, 8 cells in the third generation, and so on. The generation time is the time interval required for the cells (or population) to divide.
G (generation time) = (time, in minutes or hours)/n(number of generations)
G = t/n
t = time interval in hours or minutes
B = number of bacteria at the beginning of a time interval
b = number of bacteria at the end of the time interval
n = number of generations (number of times the cell population doubles during the time interval)
b = B x 2n (This equation is an expression of growth by binary fission)
Solve for n:
logb = logB + nlog2
n = logb - logB
log2
n = logb - logB
.301
n = 3.3 logb/B
G = t/n
Solve for G
G = t_____
3.3 log b/B
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Example: What is the generation time of a bacterial population that increases from 10,000 cells to 10,000,000 cells in four hours of growth?