SOLUTION: A certain species of bacteria in a laboratory begins with 200 cells and has a half life every 20 minutes. How many cells of the bacteria will be left after 1 hour (60 minutes)? Wri

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Question 301757: A certain species of bacteria in a laboratory begins with 200 cells and has a half life every 20 minutes. How many cells of the bacteria will be left after 1 hour (60 minutes)? Write an equation to model the problem and then solve your equation for the given value.
Answer by nerdybill(7384) About Me  (Show Source):
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A certain species of bacteria in a laboratory begins with 200 cells and has a half life every 20 minutes. How many cells of the bacteria will be left after 1 hour (60 minutes)? Write an equation to model the problem and then solve your equation for the given value.
.
Use the exponential growth/decay formula:
P%28t%29+=+Po%2Ae%5E%28rt%29
Where
P(t) is amount after t time
Po is the initial amount
r is the rate of growth/decay
t is time
.
Using the first sentence we can determine r:
(1/2)(200) = 200e^(r*20)
1/2 = e^(r*20)
ln(.5) = r*20
ln(.5)/20 = r
-.03466 = r
.
Our equation then is:
P%28t%29+=+Po%2Ae%5E%28-.03466t%29
Now, we can answer:
How many cells of the bacteria will be left after 1 hour (60 minutes)?
P%28t%29+=+200%2Ae%5E%28-.03466%2A60%29
P%28t%29+=+25+
25 cells left after 60 minutes