SOLUTION: A certain radioactive isotope has leaked into a small stream. Three hundred days after the​ leak, 13​% of the original amount of the substance remained. Determine the&#
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Question 1108262: A certain radioactive isotope has leaked into a small stream. Three hundred days after the leak, 13% of the original amount of the substance remained. Determine the half-life of this radioactive isotope. Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! A=Aoe^(-kt)
A/Ao=0.13
0.13=e^(-k*300)
ln both sides
-2.040=-300k
k=2.040/300=0.0068
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Now do it when A/Ao=1/2 and solve for t
ln (1/2)=e^-(.0068*t)
-0.693=-0.0068t
t=101.91 days
This makes sense, because 3 half lives is 300 days
Three half lives leaves about 1/8 left, and 13% is about 1/8.
