The amount of a radioactive substance remaining after t years is given by the function f of t is equal to m times 0 point 5 raised to the t over h power , where m is the initial mass and h is the half-life in years. Iron has a half-life of 2 point 7 years. Which equation gives the mass of a 200 mathrm mg iron sample remaining after t years, and approximately how many milligrams remain after 12 years?
Answer
A
f of t is equal to 2 point 7 times 0 point 5 raised to the t over 200 power ; 2 point 6 mathrm mg
B
f of t is equal to 200 times 0 point 5 to the t th power ; 0 point 0 5 mathrm mg
C
f of t is equal to 200 times 0 point 5 raised to the t over 2 point 7 power ; 9 point 2 mathrm mg
D
f of t is equal to 2 point 7 times 0 point 5 to the t th power ; 0 point 0 0 0 7 mathrm mg
Explanation
In the half-life model, m is the initial mass and h is the half-life. Substituting m = 200 mg and h = 2.7 years gives f(t) = 200(0.5)^(t/2.7). After 12 years, f(12) = 200(0.5)^(12/2.7) ≈ 9.2 mg, so the matching choice is the equation with about 9.2 mg remaining.
AI-written and checked against the verified answer.