Question

The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. Iron has a half-life of 2.7 years. Which equation gives the mass of a 200 mg iron sample remaining after t years, and approximately how many milligrams remain after 12 years?

Answer 1

The model is m(t) = m(1/2)^{t/h}. With m = 200 mg and h = 2.7 yr,

m(t) = 200(1/2)^{t/2.7}.

After 12 years:

m(12) = 200(1/2)^{12/2.7} ≈ 200(0.04594) ≈ 9.2 mg (about 9.19 mg).