MathBench > Microbiology

In search of Exact Doubling Time

Let's bust some exponents

So let's try using these rules where we ran into trouble before. Recall that we got as far as finding the log in our equation -- now we can bust right past it...

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What is the doubling time?
(10 million -> 70 million in 1 hour)

  Hint Explanation
Substitute in the known info 70 million = 10 million * 2n
Divide both sides by initial population 7 = 2n
Bust that exponent log(7) = n * log(2)
This looks complicated, but really all you need is a calculator 0.84 = n * 0.30
Now some rearranging... n = 0.84 / 0.30 = 2.8
So there were 2.8 generations in 60 minutes, so.... 60 / 2.8 = 21.4 minutes each!!

Bottom line: logs plus a calculator are a biologist's best friend....