59 minutes
Explanation:
There is 1 hour (equivalent to 60 minutes) between 11.00pm and midnight.
Using the formulae; P <em>(future</em>) = P <em>(present)</em> * (1 + <em>i</em>)ⁿ where
P <em>(Future) </em>= Future Population
P <em>(Present)</em> = Present Population
<em>i</em> = Growth Rate
n = Number of generations
The bottle was full after 60 minutes and it was filed by the following number of bacteria
P<em>(future) </em>= 1 * (1+1)⁶⁰ = 1,152,921,504,606,846,976
A half-filled bottle would have half the number = 576,460,752,303,423,488
Using the same formulae to find after how many generations do we get to this number;
576,460,752,303,423,488 = 1 * (1+1)ⁿ
(576,460,752,303,423,488) / 1 = (2)ⁿ
n = log₂ (576,460,752,303,423,488)
n = 59
This means the bottle got full at 59 minutes.
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