SOLUTION: A bacteria culture has an initial population of 10000. If its population declines to 3000 in 2 hours, what will the population be at the end of 4 hours?

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Question 40257: A bacteria culture has an initial population of 10000. If its population declines to 3000 in 2 hours, what will the population be at the end of 4 hours?
Answer by fractalier(2101) About Me  (Show Source):
You can put this solution on YOUR website!
Well if we assume exponential population decay (quite an assumption but I think that's what you need here)...our equation is
P(t) = P(0)*e^rt
Now plug in what we are given and solve for the rate, r...here goes...
3000 = 10000*e^(2r)
e^(2r) = .3
ln e^2r = ln .3
2r = ln .3
r .5 ln .3
r = -.6
Now we plug that back into the original equation to find P(t)...
P(t) = P(0)*e^rt
P(t) = 10000*e^(-.6*4)
P(t) = 10000*e(-2.4)
P(t) = 907