Refer to the model $Q(t)=Q_{0} e^{-0.000121 t}$ used for radiocarbon dating.
A sample from a mummified bull was taken from a pyramid in Dashur, Egypt. The sample shows that $68 \%$ of the carbon-14 still remains. How old is the sample? Round to the nearest year.
Part: 0 / 3
Part 1 of 3
The quantity $Q(t)$ of carbon-14 in the sample is $68 \%$ of $Q_{0}$.
\[
\text { I } Q_{0}=Q_{0} e^{-0.000121 t} \times 5
\]
Answer
Final Answer: The sample is approximately \(\boxed{2713}\) years old.
Step 1 ：The problem is asking for the time \(t\) when the amount of carbon-14 in the sample is \(68\%\) of the original amount. This can be represented by the equation \(0.68Q_{0}=Q_{0} e^{-0.000121 t}\).
Step 2 ：We can solve this equation for \(t\) by setting \(Q_{0} = 1\) and \(Q = 0.68\).
Step 3 ：Solving the equation gives \(t = 2712.536023173541\).
Step 4 ：Rounding to the nearest integer gives \(t = 2713\).
Step 5 ：Final Answer: The sample is approximately \(\boxed{2713}\) years old.
