A hypothetical strain of bacteria doubles every two minutes (exponential growth). One single bacterium was put in a sealed bottle at 8:00 AM, and the bottle was filled at exactly 10:00 AM. What time was the bottle half full?

Question

A hypothetical strain of bacteria doubles every two minutes (exponential growth).  One single bacterium was put in a sealed bottle at 8:00 AM, and the bottle was filled at exactly 10:00 AM.  What time was the bottle half full?

anonymous · Answer

Sorry there's not enough information to answer the question - how about the size of the hypothetical bacteria and the volume of the bottle?

koikkara · Answer

Ohh, well i assumes full to be by.....09:58 am.....

anonymous · Answer

I don't think that we need to know the volume of the bottle. 

I think we can assume that however many bacteria are in the bottle at 10AM, 
that is when the bottle is completely full. 

So, we find out how many bacteria are in the bottle, at 10AM, 
we divide that number by 2, 
and that is the number of bacteria, inside the bottle, when the bottle is HALF full.

If the bottle is HALF full, when there are X number of bacteria, 
then we just have to figure out the time of day, when there is X number of bacteria, in the bottle. 

~~~~~~~~~~~~~~~

But I have read article after article, 
page after page, 
of nothing but functions and exponential growth, 

and my head is spinning. 

I'd really like to know how to solve this problem. 

If ANYONE out there can demonstrate, that would be great.