MathBench > Microbiology

Frank Gets Messy: in search of Exact Doubling Time

Let's bust some exponents

logs knock exponents down to multiplication, and

logs knock multiplication down to addition.

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...

Turn on javascript to make this table interactive.

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

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

Maybe I should have said, logs plus a calculator are a biologist's best friend....