SOLUTION: A radioactive substance with an initial mass of 300mg has a half life of 2 years. a) Write an equation to model the mass of the material over time. b) How long will it take for

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Question 805657: A radioactive substance with an initial mass of 300mg has a half life of 2 years.
a) Write an equation to model the mass of the material over time.
b) How long will it take for the mass to decay to 1/3 of it's original amount?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A radioactive substance with an initial mass of 300mg has a half life of 2 years.
a) Write an equation to model the mass of the material over time.
A = 300*2^(-t/2)
:
b) How long will it take for the mass to decay to 1/3 of it's original amount?
300*2^(-t/2) = 100
2^(-t/2) = 100%2F300
ln(2^(-t/2) = ln%28100%2F300%29
-t%2F2*ln(2) = ln%28100%2F300%29
-t%2F2*.693 = -1.0986
-t%2F2 = %28-1.0986%29%2F.693
-t%2F2 = -1.585
t = -2 * -1.585
t = 3.17 days