A scientist is experimenting with bacteria that are one micron in diameter and that reproduce by dividing every minute into two bacteria. At 12:00 PM, he puts a single organism in a container. At precisely 1:00 PM, the container is full.
At what time was the container half full?
How big was the container?
I guess 12:59
ReplyDeleteThe container was half full at 12:59 (one minute to double and fill the space).
ReplyDeleteThe number of bacteria in the container is 2^n where n is the number of minutes elapsed. The full container has 2^60 (two to the sixtieth power), or approximately 1.153×10^18 bacteria. Since one micron (one millionth of a meter) is 1×10^-4 centimeters, each bacterium occupies a volume of about 1×10^-12 cubic centimeters. Multiplying times the number of organisms, we conclude that the container had a capacity of 1.153×10^6 cc or 1,153 liters. The container was slightly bigger than one cubic meter.