Question

the amount of a radioactive substance remaining after t years is given by the function f(t)=m(0.5)^(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?
o f(10)=50(0.5)^(10/5.3); 13.5 mg
o f(10)=50(0.5)^(0.5); 34.6 mg
o f(10)=5.3(0.5)^5; 0.2 mg
o f(10)=5.3(0.5)^(0.2); 4.6 mg

Explanation:

Step1: Identify values

Given $m = 50$ (initial mass), $t=10$ (time in years), $h = 5.3$ (half - life in years). The formula is $f(t)=m(0.5)^{\frac{t}{h}}$.

Step2: Substitute values

Substitute the values into the formula: $f(10)=50(0.5)^{\frac{10}{5.3}}$.

Step3: Calculate the exponent

$\frac{10}{5.3}\approx1.8868$.

Step4: Calculate the power of 0.5

$(0.5)^{1.8868}\approx0.27$.

Step5: Calculate the final result

$f(10)=50\times0.27 = 13.5$ mg.

Answer:

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