Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay.
We have the following equation representing the half-life decay:
[tex]A=A_o\times2^{(-\frac{t}{t_{half}})_{}_{}}[/tex]A is the resulting amount after t time
Ao is the initial amount = 50 mg
t= Elapsed time
t half is the half-life of the substance = 14.3 days
We replace the know values into the equation to have an exponential decay function for a 50mg sample
[tex]A=\text{ 50 }\times2^{\frac{-t}{14.3}}[/tex]That would be the answer for a)
To know the P-32 remaining after 84 days we have to replace this value in the equation:
[tex]\begin{gathered} A=\text{ 50 }\times2^{\frac{-84}{14.3}} \\ A=0.85\text{ mg} \end{gathered}[/tex]So, after 84 days the P-32 remaining will be 0.85 mg
