SOLUTION: A radioactive substance has a half-life of 60 years. There is an accident that exposes a town with the radioactive substance. The area will be safe after 95% of the substance has d

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A radioactive substance has a half-life of 60 years. There is an accident that exposes a town with the radioactive substance. The area will be safe after 95% of the substance has d      Log On


   

Question 611874: A radioactive substance has a half-life of 60 years. There is an accident that exposes a town with the radioactive substance. The area will be safe after 95% of the substance has decayed. How many years will that take?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A radioactive substance has a half-life of 60 years.
There is an accident that exposes a town with the radioactive substance.
The area will be safe after 95% of the substance has decayed. How many years will that take?
:
The radioactive decay formula A = Ao*2^(-t/h) where:
A = amt after t time (.05)
Ao = initial amt (1)
t = time of decay
h = half-life of substance (60)
:
1*2^(-t/60) = .05
-t%2F60ln(2) = ln(.05)
-t%2F60 = ln%28.05%29%2Fln%282%29
-t%2F60 = -4.322
t = -60 * -4.322
t = 259.3 yrs