Question

The half life of Mercury-203, which is used in certain medical procedures, is approximately 47 days. If a shipment of 400 mg is made to a medical company, how much Mercury-203 will be left after two weeks?
Approximately 388 mg.


Approximately 325 mg.


Approximately 39 mg.


Approximately 3.37 mg.

Answer 1

The half-life is 47 days, which means that for any starting amount $a_0$ of Hg-203, we're left with $\dfrac{a_0}2$ after this amount of time.

$\dfrac{a_0}2=a_2e^{47k}\implies\dfrac12=e^{47k}\implies-\dfrac{\ln2}{47}=k$

So, the amount of Hg-203 $a(d)$ left after $d$ days is given by

$a(d)=a_0e^{-(\ln2)/47\,d}$

2 weeks = 14 days, so if we start with 400 mg, after two weeks we end up with

$a(14)=400e^{-(\ln2)/47\cdot14}\approx325.38$ mg