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?

tkhunny · Answer

You have to reach out and grab these!!  It's just staring at you.

9:58 AM - Almost by inspection.  You tell me why.

anonymous · Answer

I'm sorry can you please explain how you got the answer

tkhunny · Answer

It doubles every two minutes.  How much was there in the jar two minutes ago?

anonymous · Answer

still don't get it. The bottle is throwing me off

tkhunny · Answer

Don't use a bottle.

1, 2, 4, 8, 16, 32, ...  This is doubling, right?  Every two minutes we move up another slot.

Suppose we start at some other point and go backwards?

1024, 512, 256, 128, 64, 32, ...  This is doubling backwards, right?  Every two minutes we move down another slot.  If we pick ANY point, even a full bottle, there will be one-half of that two minutes earlier.

anonymous · Answer

oh i understand now thank you