ANSWER:
C. approx. 10,710 years
STEP-BY-STEP EXPLANATION:
We have that the function that models the situation is the following:
[tex]Q(t)=Q_0\cdot e^{-kt}[/tex]
We substitute each value and calculate the value of t, like this:
[tex]\begin{gathered} 5=500\cdot \:e^{-0.00043t} \\ \\ e^{-0.00043t}=\frac{5}{500} \\ \\ -0.00043t=\ln \left(\frac{1}{100}\right) \\ \\ t=\frac{\ln\left(\frac{1}{100}\right)}{-0.00043} \\ \\ t=10709.6981\approx10710\text{ years} \end{gathered}[/tex]
So the correct answer is C. approx. 10,710 years
