Step 1
Given;
[tex]Q(t)=Q_oe^{-kt}[/tex]From the question;
[tex]\begin{gathered} Q(t)=5 \\ Q_o=500 \\ k=0.00043 \end{gathered}[/tex][tex]\begin{gathered} 5=500e^{-(0.00043t)} \\ \frac{5}{500}=e^{-0.00043} \\ 0.01=e^{-0.00043} \\ -0.00043t=\ln \left(\frac{1}{100}\right) \\ t=\frac{2\ln \left(10\right)}{0.00043} \\ t=10709.69810 \\ t=\text{ approximately 10710 years} \end{gathered}[/tex]Answer; Option A
