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