A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 75 cells. Find the number of cells after 2 hours.
A) $P = 16,800$
B) $P = 104,800$
C) $P = 144,800$
D) $P = 4,800$
E) $P = 124,800$

Question

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 75 cells. Find the number of cells after 2 hours. 
A) $P = 16,800$
B) $P = 104,800$
C) $P = 144,800$
D) $P = 4,800$
E) $P = 124,800$

Quizplus · Accepted Answer

The population doubles every 20 minutes, so in 2 hours (which is 120 minutes), there are 6 doubling periods. The population after 2 hours is $75 \times 2^6 = 75 \times 64 = 4,800$.

A Common Inhabitant of Human Intestines Is the Bacterium Escherichia P=16,800P = 16,800P=16,800

A Common Inhabitant of Human Intestines Is the Bacterium Escherichia $P = 16,800$