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)) \\ (5)/(500)=e^(-0.00043) \\ 0.01=e^(-0.00043) \\ -0.00043t=\ln \left((1)/(100)\right) \\ t=(2\ln \left(10\right))/(0.00043) \\ t=10709.69810 \\ t=\text{ approximately 10710 years} \end{gathered}`

Answer; Option A