SOLUTION: 2. Bacteria grow by cell division. If each cell divides into 2 in every 2 minutes how many cells will exist after 32 minutes? Assume there was only one cell at the beginning
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-> SOLUTION: 2. Bacteria grow by cell division. If each cell divides into 2 in every 2 minutes how many cells will exist after 32 minutes? Assume there was only one cell at the beginning
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Question 302209: 2. Bacteria grow by cell division. If each cell divides into 2 in every 2 minutes how many cells will exist after 32 minutes? Assume there was only one cell at the beginning Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! 2. Bacteria grow by cell division. If each cell divides into 2 in every 2 minutes how many cells will exist after 32 minutes? Assume there was only one cell at the beginning
.
C(t) = Co*e^(rt)
where
C(t) number of cells after t time
Co initial number of cells
r is rate of growth
t is time in minutes
.
To determine r:
We use:"each cell divides into 2 in every 2 minutes"
C(t) = Co*e^(rt)
2 = 1*e^(r*2)
2 = e^(r*2)
ln(2) = r*2
ln(2)/2 = r
.
Our equation is now:
C(t) = e^(ln(2)t/2)
Now, we can answer "how many cells will exist after 32 minutes?"
C(32) = e^(ln(2)(32)/2)
C(32) = e^(ln(2)(16))
C(32) = 65536
