SOLUTION: A bacteria culture initially contains 2000 bacteria and doubles every half hour. The formula for the population is p(t)=2000e^kt for some constant(k) . (You will need to find (k)

Question 246250: A bacteria culture initially contains 2000 bacteria and doubles every half hour. The formula for the population is p(t)=2000e^kt for some constant(k) . (You will need to find (k) to answer the following.)

Find the size of the baterial population after 80 minutes?

Find the size of the baterial population after 6 hours?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A bacteria culture initially contains 2000 bacteria and doubles every half hour. The formula for the population is p(t)=2000e^kt for some constant(k) . (You will need to find (k) to answer the following.)
.
Consider t (time) in units of minutes.
p(t)=2000e^kt
4000=2000e^(30k)
2 = e^(30k)
ln(2) = 30k
ln(2)/30 = k
.
Find the size of the baterial population after 80 minutes?
p(80)=2000e^(80ln(2)/30)
p(80)=12699
Find the size of the baterial population after 6 hours?
6 hours = 6*60 = 360 minutes
p(360)=2000e^(360ln(2)/30)
p(360)=8192000

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