# Calc

A sample of a radioactive substance decayed to 93.5% of its original amount after a year.

a) What is the half-life of the substance?
? years

(b) How long would it take the sample to decay to 10% of its original amount?
? years

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1. a) Let the half life in years be H
2^-(1/H) = 0.935
Solve that for H.
-1/H log 2 = log 0.935
-1/H = -0.09696
H = 10.31 years

b) Solve 2^-(t/10.31) = 0.10
t will be the time required to decasy to 10% activity

You could also solve
(0.935)^t = 0.1
The answer should be the same either way you do it: about 30 years.

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2. Thank you!

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