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...
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What is the doubling time?
(10 million -> 70 million in 1 hour)
Hint | Explanation | |
sub in the known info | 70 million = 10 million * 2^{g} | |
divide out the initial population | 7 = 2^{g} | |
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....
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