Description
A culture starts with 8100 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.)
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
n(t) = |
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
hr
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Explanation & Answer
Thank you for the opportunity to help you with your question!
a)
We need to find the rate constant. The general formula is:
P = A0e^(kt)
100 = 81e^(k*1)
100/81 = e^k
ln(100/81) = k
k = .211
So the equation is
n(t) = 8100*e^(0.211t)
b) n(t) = 8100*e*(.211*2)
n(t) = 8100*e^.422
n(2) = 12352.57
c)
16200 = 8100*e^(0.211t)
ln(2) = 0.211t
t(2x) = ln(2)/0.211 = 3.3 hrs
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