Respuesta :
Given:
a,) The half-life of iodine-131 is 8 days.
b.) A hospital receives a shipment of 200 grams.
c.) Determine how much would remain after 32 days.
We will be using the following formula:
[tex]\text{ N}_t\text{ = N}_0(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}[/tex]Where,
[tex]\begin{gathered} \text{ N}_t\text{ = Quantity of the substance remaining} \\ \text{ N}_0\text{ = Initial quality of the substance = 200 grams} \\ \text{ t = Time elapsed = 32 days} \\ \text{ t}_{\frac{1}{2}}\text{ = Half life of the substance = 8 days} \end{gathered}[/tex]We get,
[tex]\text{N}_t\text{ = N}_0(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}[/tex][tex]\text{ N}_t\text{ = \lparen200\rparen\lparen}\frac{1}{2})^{\frac{32}{8}}[/tex][tex]\text{ N}_t\text{ = 200\lparen}\frac{1}{2})^4[/tex][tex]\text{ N}_t\text{ = 200\lparen}\frac{1}{16})\text{ = }\frac{200}{16}[/tex][tex]\text{ N}_t\text{ = 12.5 grams}[/tex]Therefore, in 32 days, only 12.5 grams of Iodine-131 will remain.
