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?

; 2.6 mg
f(t)=2.7(0.5)t; 0.0007 mg
f(t)=200(0.5)t; 0.05 mg
; 9.2 mg

Answer 1

General formula: f(t) = m(1/2)^{t/h}. With m = 200 mg and h = 2.7 y:

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

After 12 years: f(12) = 200(1/2)^{12/2.7} ≈ 200(1/2)^{4.444…} ≈ 9.2 mg.