Question

The amount of a sample remaining after t days is given by the equation p(t)=A(1/2)^t/h, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?

Answer 1

9.4 days

Explanation:

Answer 2

9.4 days

Explanation:

Filling in the given numbers, we can solve for t:

0.18 = 1·(1/2)^(t/3.8)

log(0.18) = (t/3.8)log(1/2)

t = 3.8·log(0.18)/log(0.50) ≈ 9.4 . . . . days

The best estimate of the age of the sample is 9.4 days.