SOLUTION: The half-life of a substance is the time it takes for half of the substance to remain after natural decay. Radioactive water (tritium) has a half-life of 12.6 years. How long will

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Question 202639: The half-life of a substance is the time it takes for half of the substance to remain after natural decay. Radioactive water (tritium) has a half-life of 12.6 years. How long will it take for 85% of a sample to decay?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The half-life of a substance is the time it takes for half of the substance
to remain after natural decay. Radioactive water (tritium) has a half-life
of 12.6 years. How long will it take for 85% of a sample to decay?
:
The half life formula:
A = Ao
where:
A = the resulting amt after t (yrs in this case)
Ao = initial amt
t = time (yrs)
h = half-life of substance (yrs)
:
Let initial amt: Ao = 1, then find A: 1.0 - .85 = .15
:
1*2^(-t/12.6) = .15
Find the log of both sides
.301-t%2F12.6 = -.8239
-.301t%2F12.6 = -.8239
Multiply both sides by 12.6
-.301t = -.8239 * 12.6
:
-.301t = -10.381
t = %28-10.381%29%2F%28-.301%29
t = 34.49 yrs
:
:
Check solution on a calc: enter 2^(-34.49/12.6) = .1499 ~ .15