Answer :
Given:
The initial amount of the radioactive sample is,
[tex]m=200\text{ g}[/tex]The half-life is,
[tex]t_{\frac{1}{2}}=45\text{ days}[/tex]The total time span is,
[tex]t=360\text{ days}[/tex]To find:
How many grams will be left after 360 days?
Explanation:
The number of half-life within the given time span is,
[tex]\begin{gathered} n=\frac{t}{t_{\frac{1}{2}}} \\ n=\frac{360}{45} \\ n=8 \end{gathered}[/tex]The sample left over after this time is,
[tex]\begin{gathered} m^{\prime}=m\times(\frac{1}{2})^n \\ =200\times(\frac{1}{2})^8 \\ =200\times\frac{1}{256} \\ =0.78\text{ g} \end{gathered}[/tex]Hence, the leftover amount after the time is 0.78 g.