Question 148605: A culture of yeast doubles in size every 20 minutes. The size of the culture is now N0. Find its size in 12 hours. How do you solve these problems?
Sugar is put in a large quantity of water and the mixture is stirred. After 2 minutes, 50% of the sugar has dissolved. How much longer will it take until 90% of the sugar has dissolved?
I am really having trouble and I need your assistance.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A culture of yeast doubles in size every 20 minutes. The size of the culture is now No. Find its size in 12 hours.
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A(t) = No(2)^(t/20) where t is the number of hours
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A(12) = No(2)^(12*(60/20)) = No*2^36 = appox. 6.87..x 10^10*No
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Sugar is put in a large quantity of water and the mixture is stirred. After 2 minutes, 50% of the sugar has dissolved. How much longer will it take until 90% of the sugar has dissolved?
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If 50% has dissolved after 2 minutes, 50% remains after two minutes.
You want to know how long till only 10% of No remains.
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EQUATION:
When does No(1/2)^(x/2) = 0.1No
(1/2)^(x/2) = 0.10
Take the log of both sides to get:
(x/2)*log(1/2) = log 0.1
(x/2) = 3.321928...
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Number of minutes = 2*3.321978.. = 6.643856...
This is total time including the 1st two minutes.
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Cheers,
Stan H.
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