SOLUTION: A culture starts with 9000 bacteria. After one hour the count is 10,000. (a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three de

Question 979496: A culture starts with 9000 bacteria. After one hour the count is 10,000.
(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
n(t) =
b. How many hours will the number of bacteria double?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
A=Ao{1+r}^t; t=hours
10000=9000(l+r)^t
divide by 9000 and take ln of both sides
ln (10/9)=t ln (1+r)
0.1054=ln(1+r)
raise both sides to e power
1.111=1+r
r=0.111 or 11.1%
ln2=t ln (1.111)
0.693=t * 0.10536
t=6.578 hours or about 6 hours 35 minutes
Check:
1.111^6.578=2

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