Question 602310: At the beginning of an experiment, a culture contains 1000 bacteria . Five hours later, there are 7600 bacteria. Assuming that the bacteria grow exponentially, how many bacteria will there be after 24 hours?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! At the beginning of an experiment, a culture contains 1000 bacteria . Five hours later, there are 7600 bacteria. Assuming that the bacteria grow exponentially, how many bacteria will there be after 24 hours?
.
Exponential growth equation:
p = e^(kt)
where
p is amount after time t
k is a constant
t is time
.
From:"At the beginning of an experiment, a culture contains 1000 bacteria . Five hours later, there are 7600 bacteria." we get:
7600 = 1000e^(5k)
7600/1000 = e^(5k)
7.600 = e^(5k)
ln(7.600) = 5k
ln(7.600)/5 = k
0.40563 = k
.
Our "general equation" for growth then is:
p = e^(0.40563t)
which we use to solve:
how many bacteria will there be after 24 hours?
p = e^(0.40563*24)
p = 16900 (answer)
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