The rate of exponential growth can be described with the mean growth rate constant.
The mean growth rate constant (k) is the number of generations (n) per unit of time (t). The mean growth rate constant 'k' is the number of generations 'n' per unit of time 't'.
k = n / t'k' is equal to 'n' divided by 't'
In case of microorganisms it is usually expressed as generations per hour.
If you know the number of bacteria Nt and the initial number of bacteria N0 you can calculate the growth rate with the following formula.If you know the number of bacteria N 't' and the initial number of bacteria N zero you can calculate the growth rate with the following formula.
k = log2 (Nt / N0) / t'k' is equal to logarithm two of N 't' divided by N zero, divided by 't'
or when using log10logarithm 10:
k = log10(Nt / N0) / 0.301 t'k' is equal to logarithm 10 of N 't' divided by N zero, divided by 0.301 times 't'
Note that it doesn't matter if we know the precise number of microorganisms or an indirect factor such as the optical density of a culture tube because the k is a relative value.
In a logarithmic growth chart the growth rate is the represented by the slope of the exponential phase.
Check out the generation time page to learn how the generation time is calculated.