Bacterial generation time

Bacterial growth in exponential phase, N = N₀ × 2^(t/g), where g is the generation time. Two counts and their interval give g = t / log₂(N/N₀). The two other modes give the population after a duration and the time to reach a target, with the number of generations and the specific growth rate µ.

The number of elapsed generations is log₂(N/N₀). The specific growth rate µ = ln 2 / g is the one in dN/dt = µN, in min⁻¹ or h⁻¹.

Generation time g

the duration of one population doubling in exponential phase. E. coli in rich medium, about 20 minutes (µ ≈ 2.1 h⁻¹); a yeast, 90 minutes.

Exponential phase

the regime where cells divide at a constant pace, the only phase the model describes.

Lag and plateau

the lag precedes the exponential phase (cells adapt without dividing), the plateau follows it (nutrients exhausted, waste accumulated). Two regimes outside the model.

CFU

colony-forming unit: the count of viable cells by plating, the reference measure of enumeration.

Idealised synchronous growth at a constant rate, valid in established exponential phase, in non-limiting medium and at stable temperature. Lag, plateau, decline and diauxic growth (two substrates, two slopes) are outside the model. Optical density measures total biomass, dead cells included, CFU only the viable cells; the two g values can differ.

Half of the biomass appears during the last generation: a culture half-turbid at 18:00 is fully turbid at 18:20. An overnight culture (12 h at g = 20 min) is 36 doublings, a factor of 7 × 10¹⁰.

g characterises a strain in a given medium and varies with temperature, medium and aeration. Three or more points aligned on a log scale confirm the exponential phase (linear regression on log(N)).