The generation time is the time interval required for the cells (or population) to divide.
G (generation time) =t (time, in minutes)/n(number of generations)
G = t/n
t = time interval in minutes = 180 minutes
B = number of bacteria at the beginning of a time interval = 500 cells
b = number of bacteria at the end of the time interval = 2,56,000 cells
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
G = 180
3.3 log 256000 –log500
=180 / 8.943
G = 20.12 minutes per generation