A culture starts with 8600 bacteria. After one hour the count is 10,000.

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(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
Apr 17th, 2015

Denote the number of bacteria by n(t). Then n(t) = n_0 e^(kt) is an exponential function.

n(0) = 8600 = n_0, so n(t) = 8600 e^(kt).

Since n(1) = 8600 e^k = 10000, e^k = 10000/8600 = 1.163, k = ln(1.163) = 0.151, and n(t) = 8600 e^(0.151t).

(b) n(2) = 8600 e^(0.151*2) = 11600

(c) n(t) = 8600 e^(0.151t) = 2*8600 when e^(0.151t) = 2; 0.151t = ln(2)

t = ln(2)/ 0.151 = 4.6 hours

Apr 17th, 2015

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Apr 17th, 2015
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Apr 17th, 2015
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