First, we have that on day 0, the percent of remaining iodine is 100%. This percent reaches 50% on day 8; so the half-life of iodine-131 is 8 days.
With this data, we can find the remaining amount based on the following formula:
[tex]N(t)=N_o\cdot(\frac{1}{2})^{\frac{t}{half-life_{}}}\begin{cases}N_o=initial\text{ quantity} \\ t=\text{time (days)} \\ half-life=half-life\text{ (days)}\end{cases},^{}^{}[/tex]
We have that the initial quantity is 50 grams and the time is 32 days. Replacing all data, we obtain:
[tex]N(t)=50\cdot(\frac{1}{2})^{\frac{32}{8}}=50\cdot(\frac{1}{2})^4=\frac{25}{8}=3.125\text{ g.}[/tex]
So, the remaining quantity of iodine-131 after 32 days is 3.1 grams.
