The generation time gives a good estimation of the health of your culture and the optimisation of the growth conditions. It will also enable you to estimate when a specific population size will be reached.
To calculate the generation time, you will need to measure the population size (N) at two different time points during the exponential phase, keeping in mind the interval t during these timepoints.
Let's call the population at the first timepoint N0 and at the second timepoint Nt, with n the number of generations. Let's call the population at the first timepoint N zero and at the second timepoint N t, with 'n' as the number of generations.
From the formula explained above:
Nt = N0 x 2n (each cell at N0 has doubled in each generation until reaching Nt) N t is equal to N zero multiplied by two to the power of 'n'. Each cell at N zero has doubled in each generation until reaching N 't'.
Thus:
log(Nt) = log(N0) + n x log(2)logarithm of N 't' is equal to logarithm of N zero plus 'n' times logarithm of 2
We are looking for the number of generation n:
n = log(Nt) - log(N0) / log(2)n is equal to logarithm of N 't' minus logarithm of N zero divided by logarithm of 2
n = log(Nt) - log(N0) / 0.301n is equal to logarithm of N 't' minus logarithm of N zero divided by 0.301
n = 3.3 x log(Nt / N0)n is equal to 3.3 times logarithm of N 't' divided by N zero
By counting the population at N0 and Nt N zero and N 't'you have now calculated the number of generations which occurred in the interval. By dividing the time of the interval t by the number of generations, you will get the generation time (for 1 generation).
G = t / n Capital G is equal to 't' divided by 'n'
Thus in one equation:
G = t / (3.3 x log (Nt / N0)Capital G is equal to 't' divided by 3.3 times logarithm of N 't' divided by N zero
Check out the growth rate constant page to learn how this relates the growth rate constant.