Graph (a) represents the growth of a microbial population using real (arithmetic) numbers.  Note the J-shape and that it is difficult to determine actual cell numbers at the beginning of the curve.  Graph (b) is a semi-logarithmic representation of the same growth in which each division on the Y-axis is ten times larger than the last.  Note that in this graph, the population is a straight line.  Both curves represent bacterial growth in an open (continuous) culture where waste and dead cells are constantly removed and fresh medium is constantly added.

This graph represents the four-phase pattern of population growth when bacteria are raised in a batch (closed) culture such as a petri dish or test tube where no additional nutrients are added, no waste or dead cells are removed and where there is no additional space.

The lag phase occurs after microbes have been added and represents the period of time the organisms need to adapt to the new environment.  Population growth at this time is slight, very close to 0.

The log phase represents the period of optimal population growth.  Eventually, however, the microbes approach the upper limit to their continued growth called the carrying capacity (k).  If the population grows beyond k it will run out of nutrients and space and may crash.

At this point, bacterial population levels out and population growth nears 0 again.  This stage, called the stationary phase, may last for a long period of time.  In a device called a chemostat used in the fermentation and pharmaceutical industries, bacterial growth is kept in the stationary phase.

Ultimately, waste and dead cells begin to accumulate, causing the death phase.  The population declines during this phase though it does not completely crash.  Spore formers can persist beyond this stage and can regenerate a population if conditions once again become favorable.