A culture starts with 8100 bacteria. After one hour the count is 10,000. (a) Fin

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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.)
n(t) =

(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.) 

(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.) 


Jul 15th, 2015

Thank you for the opportunity to help you with your question!


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


16200 = 8100*e^(0.211t)

ln(2) = 0.211t

t(2x) = ln(2)/0.211 = 3.3 hrs

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 15th, 2015

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