Question

he 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. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?

Answer 1

The decay model is A(t) = m (1/2)^{t/h}. With m = 50 mg and h = 5.3 yr:

A(t) = 50(1/2)^{t/5.3}.

After 10 years:

A(10) = 50(1/2)^{10/5.3} ≈ 50(1/2)^{1.8868} ≈ 50(0.2706) ≈ 13.5 mg.