Question

Bacteria multiply by division.One bacterium becomes two. Then two divide into four the four divide into eight and so on For a certain strain of bacteria the time for this division process is one minute (the doubling time).If you put one bacterium in a bottle at 11:00 pm by midnight the entire bottle will be full.At what time will the bottle be half full?(Hint:calculate population after 60 min)

Answer 1

59 minutes

Explanation:

There is 1 hour (equivalent to 60 minutes) between 11.00pm and midnight.

Using the formulae; P (future) = P (present) * (1 + i)ⁿ where

P (Future) = Future Population

P (Present) = Present Population

i = Growth Rate

n = Number of generations

The bottle was full after 60 minutes and it was filed by the following number of bacteria

P(future) = 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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