SOLUTION: The count of bacteria in a culture was 200 after 2 hours and 24,000 after 8 hours. What is the relative growth rate of the bacteria population, as a percentage?

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Question 1037372: The count of bacteria in a culture was 200 after 2 hours and 24,000 after 8 hours. What is the
relative growth rate of the bacteria population, as a percentage?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let P%28t%29+=+P%5B0%5D%2A%281%2Br%29%5Et, where P%5B0%5D is the initial count, and r is the relative growth rate.
==> P%282%29+=+200+=+P%5B0%5D%2A%281%2Br%29%5E2 and P%288%29+=+24000+=+P%5B0%5D%2A%281%2Br%29%5E8
Dividing the second equation by the first equation (effectively canceling P%5B0%5D), we get
120+=+%281%2Br%29%5E6
==> r+=+root%286%2C120%29+-+1+=+1.220906.
Therefore the relative growth rate r is 122.0906%.