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# Doubling math question?

If a certain bacteria can double its population every hour, how long will it take for the population of the bacteria to reach 16384 assuming that there is one bacterium to start with?

Okay so i know the long way to solve this, just to keep doubling it, but is there a shorter way?

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- Anonymous9 years agoFavorite Answer
There will be 2^n bacteria after n hours when started with 1.

2^n = 16384

You do the calculations.

- Anonymous9 years ago
yes, using a scientific calculator and logarithms

the equation is 2 ^ N = 16384

so N (log 2) = log 16384

N = log 16384 / log 2

using my calculator gives exactly 14 hours :-)))

if you don't know what a logarithm is, then you just have to keep on doubling. sorry.

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