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. Cobalt- 60 has a half-life of about 5 point 3 years. Which equation gives the mass of a 50 milligrams Cobalt- 60 sample remaining after 10 years, and approximately how many milligrams remain?
Answer
A
f of 10 is equal to 50 times 0 point 5 raised to the 10 over 5 point 3 power ; 13 point 5 milligrams
B
f of 10 is equal to 5 point 3 times 0 point 5 to the 5th power ; 0 point 2 milligrams
C
f of 10 is equal to 5 point 3 times 0 point 5 raised to the 0 point 2 power ; 4 point 6 milligrams
D
f of 10 is equal to 50 times 0 point 5 0 raised to the 0 point 5 3 power ; 34 point 6 milligrams
Explanation
Use the decay formula f(t) = m × 0.5^(t/h), with initial mass m = 50 milligrams and half-life h = 5.3 years. After 10 years, f(10) = 50 × 0.5^(10/5.3) ≈ 13.5 milligrams. This matches choice D.
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