SOLUTION: A bacteria culture starts with 1,000 bacteria and doubles in size every 2 hours. Find an exponential model for the size of the culture as a function of time t in hours.
f(t) =
1
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f(t) =
1
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Question 354041: A bacteria culture starts with 1,000 bacteria and doubles in size every 2 hours. Find an exponential model for the size of the culture as a function of time t in hours.
f(t) =
1
Use the model to predict how many bacteria there will be after 2 days. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! A bacteria culture starts with 1,000 bacteria and doubles in size every 2 hours. Find an exponential model for the size of the culture as a function of time t in hours.
.
P = Noe^(kt)
where
P is amount after t time
No is the initial amount
.
No is 1000
P is 2000
t = 2
.
2000 = 1000e^(2k)
2= e^(2k)
ln(2) = 2k
ln(2)/2 = k
0.34657 =k
.
F(t) = 1000e(0.34657t)
.
Use the model to predict how many bacteria there will be after 2 days.
2 days in terms of hours is 48 hours
.
F(48) = 1000e(0.34657*48)
F(48) = 1000e(-16.63553)
F(48) = 1.6778*10^10
