Question

the amount of a radioactive substance remaining after \\(t\\) years is given by the function \\(f(t) = m(0.5)^{\frac{t}{h}}\\), 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?

\\(f(10) = 50(0.5)^{\frac{10}{5.3}}\\); 13.5 mg

\\(f(10) = 50(0.50)^{0.53}\\); 34.6 mg

\\(f(10) = 5.3(0.5)^{5}\\); 0.2 mg

\\(f(10) = 5.3(0.5)^{0.2}\\); 4.6 mg

Explanation:

Identify the given parameters

Using the Half-Life Calculation knowledge point

$$
LATEXBLOCK0
$$

Substitute parameters into the function

Using the Half-Life Calculation knowledge point

$$ f(10) = 50(0.5)^{\frac{10}{5.3}} $$

Calculate the remaining mass

Using the Half-Life Calculation knowledge point

$$
LATEXBLOCK1
$$

Match with the correct option

Using the Half-Life Calculation knowledge point

$$ f(10) = 50(0.5)^{\frac{10}{5.3}};\quad 13.5\text{ mg} $$

Answer:

• (A) \(f(10)=50(0.5)^{\frac{10}{5.3}};\ 13.5\text{ mg}\) (Correct answer)
• (B) \(f(10)=50(0.50)^{0.53};\ 34.6\text{ mg}\)
• (C) \(f(10)=5.3(0.5)^{5};\ 0.2\text{ mg}\)
• (D) \(f(10)=5.3(0.5)^{0.2};\ 4.6\text{ mg}\)