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
`\frac{a_0}2` after this amount of time.

`\frac{a_0}2=a_2e^(47k)\implies\frac12=e^(47k)\implies-(\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