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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​ 11:39? What fraction of the bottle is full at that​ time?

 Sep 17, 2019
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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​ 11:39? What fraction of the bottle is full at that​ time?"

 

After 1 min there are 21 bacteria.

After 2 mins there are 22 bacteria.

After 3 mins there are 23 bacteria.

...

After n mins there are 2n bacteria.

 

So after 39 mins there are 239 bacteria

After 60 mins there are 260 bacteria

 

Fraction full at 11.39 is thereferore 239/260 or  2-21

.

 Sep 17, 2019

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