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Suppose a single bacterium is placed in a bottle at 11:00 am. It grows and at 11:01 divides into two bacteria. These two bacteria each grow and at 11:02 divide into four bacteria, which grow and at 11:03 divide into eight bacteria, and so on. Now, suppose the bacteria continue to double every minute and the bottle is full at 12:00. How many bacteria are in the bottle at

11:52 ?

What fraction of the bottle is full at that time?

There will be

bacteria in the bottle at 11:52

.

The bottle will be full at

Guest Nov 9, 2017
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The number of bacteria  N minutes after 11:00   =  2^N

So when the bottle is full at noon , we will have 2^60 bacteria

And at 11:52 we will have 2^52 bacteria

So

2^52 / 2^60  =    1 / 2^8   full 1 / 256  full at 11:52

[ A little surprising, huh ?? ]

CPhill  Nov 9, 2017

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