Question

The function gives the mass, m, of a radioactive substance remaining after h half-lives. 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?

Answer 1

The equation is $f(t)=50(0.5)^{\frac {10}{5.3}}$ and approximately 13.52  milligram remains

How to determine the equation?

The missing information in the question is:

$f(t)=m(0.5)^{\frac th}$

When the mass is 50 mg, it means that:

m = 50

So, we have:

$f(t)=50(0.5)^{\frac th}$

When 10 years remain in the life of the substance, it means that:

t = 10

So, we have:

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

The half life is 5.3. So, we have

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

Evaluate the equation

f(t) = 13.52

Hence, the required equation is $f(t)=50(0.5)^{\frac {10}{5.3}}$ and approximately 13.52  milligram remains

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