Question

Radium decays according to the function Q(t) = Q0e^-kt where Q represents the quantity remaining after t years and k is the decay constant 0.00043. how long will it take for 500g of radium to decay to 5g?A. approx. 10,710 yearsB. approx. 233 yearsC. approx 2501 yearsD. approx 14,453 years

Answer 1

Step 1

Given;

$Q(t)=Q_oe^{-kt}$

From the question;

$\begin{gathered} Q(t)=5 \\ Q_o=500 \\ k=0.00043 \end{gathered}$$\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}$

Answer; Option A