SOLUTION: A bacteria culture initially contains 3000 bacteria and doubles every half hour. The formula for the population is P(t)=3000e^(kt) for some constant k. How do I solve for k?

Question 747333: A bacteria culture initially contains 3000 bacteria and doubles every half hour. The formula for the population is P(t)=3000e^(kt) for some constant k. How do I solve for k?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
The formula P(t) = P(o)e^kt t is in hours
P(o) - original amount of bacteria.
working on the principle that the culture
doubles every half an hour. The amount
after 1 hour would = 12000 bacteria
12,000 = 3,000 e^ k x 1
12,000 = 3,000 e^k
12000/3000 = e^k
4 = e^k
lge 4 = k loge e
k = loge 4
k = 1.38629

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