Question

See the picture to find the questions and multiple choice options

Answer 1

C. approx. 10,710 years

Explanation:

We have that the function that models the situation is the following:

`Q(t)=Q_0\cdot e^(-kt)`

We substitute each value and calculate the value of t, like this:

`\begin{gathered} 5=500\cdot \:e^(-0.00043t) \\ \\ e^(-0.00043t)=(5)/(500) \\ \\ -0.00043t=\ln \left((1)/(100)\right) \\ \\ t=(\ln\left((1)/(100)\right))/(-0.00043) \\ \\ t=10709.6981\approx10710\text{ years} \end{gathered}`

So the correct answer is C. approx. 10,710 years