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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

.

(Type your answer using exponential notation.)

 

The bottle will be full at

 Nov 9, 2017
 #1
avatar+98005 
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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 ?? ]

 

 

cool cool cool

 Nov 9, 2017

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