The function f(h)=m(1/2)^h gives the mass, m, of a radioactive substance remaining after h half-lives. iron has a half-life of 2.7 years. which equation gives the mass of a 200 mg iron sample remaining after y years, and approximately how many milligrams remain after 12 years? 1: f(x) = 2.7(0.5)200; 1.7 mg 2: f(x) = 200(0.5)12; 30.8 mg 3: f(x) = 200(0.5)12; 30.8 mg 4: f(x) = 200(0.185)12; 3.2 mg 5: f(x) = 200(0.774)12; 9.2 mg

If a certain initial amount, A₀, of material decays with a half-life of h, the amount of material that remains at time t is given by the exponential decay model



==================================================
Part (a)
Which equation gives the mass of a 200 mg Iron sample remaining after y years?

∴ A₀ = 200 mg , t = y  and   h = 2.7 years
so, the equation will be:

∴

====================================================

Part (b):
How many milligrams remain after 12 years?


By substitute with y = 12 in the equation obtained from (a)
∴

So, the correct answer is option ⇒ 5: f(x) = 200(0.774)^12; 9.2 mg