exponential population growth

© Eric R. Pianka
 
The late Garrett Hardin summarized geometric growth with the simple statement that "what starts  off slow, finishes in a flash."
 

Under optimal conditions, the human gut bacterium, Escherichia coli,  can double every  20 minutes.  Beginning with just  a single bacterium, grown in a chemostat at 98.6 degrees F  with ample sugar and other food, the population progresses from one to two in the first 20  minutes, then from 2 to 4 in the second 20 minutes, and then from 4 to 8 in the third 20 minutes.   So, under ideal conditions, one bacterium becomes 8 in just one hour.  If this maximal rate of  increase continues for a day and a half, after only 36 hours, a one-foot deep layer of bacteria  will cover the entire surface of the Earth (land and oceans).  In the next hour, this layer  doubles to two feet deep, then four feet deep, and in only 39 hours, the entire planet is covered  over with an 8 foot deep layer of bacteria.  Such inexorable population growth is known as  exponential or geometric growth and leads to J-shaped populatIon trajectories through time  (see following figure showing bacteria growing exponentially on an agar plate).