## Wednesday, September 13, 2006

### Fill 'er up

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?

1. I guess 12:59

2. The container was half full at 12:59 (one minute to double and fill the space).

The 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.

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