Prehistoric cave paintings were discovered in a cave in France. The paint contained $33 \%$ of the original carbon-14. Use the exponential decay model for carbon-14, $A=A_{0} e^{-0.000121 t}$, to estimate the age of the paintings. The paintings are approximately years old. (Round to the nearest integer.)

Step 1 ：The exponential decay model for carbon-14 is given by \(A=A_{0} e^{-0.000121 t}\), where \(A\) is the remaining amount of carbon-14, \(A_{0}\) is the original amount of carbon-14, and \(t\) is the time in years.

Step 2 ：In this case, we know that \(A\) is 33% of \(A_{0}\), so we can set up the equation \(0.33A_{0}=A_{0} e^{-0.000121 t}\) and solve for \(t\).

Step 3 ：By solving the equation, we find that \(t\) is approximately 9163.

Step 4 ：Final Answer: The paintings are approximately \(\boxed{9163}\) years old.