Bacterial population growth.

Bacteria grown in liquid medium are started with an inoculum (a few cells).

The cells show an initial slow growth (lag phase) followed by a period of rapid exponential growth (log phase) when the doubling time can be as short as 20 minutes. wmplayer

Nutrients eventually become limiting and cells enter the stationary phase.

A prototroph can synthesize all essential organic compounds and can be grown on minimal medium of carbohydrates and salts, while an auxotroph has lost the ability to synthesize some compounds which must be provided in the medium for the auxotroph to grow.