The paint contained 12% of the original carbon-14. use the exponential decay model for carbon-14, A=A0e^-0.000121t, to estimate the age of the paintings The paintings are approximately years old. (Round to the nearest integer.)

Step 1 ：The question is asking for the age of the paintings given that they contain 12% of the original carbon-14. The exponential decay model for carbon-14 is given by \(A=A0e^{-0.000121t}\), where \(A\) is the amount of carbon-14 remaining, \(A0\) is the original amount of carbon-14, and \(t\) is the time in years.

Step 2 ：Since the paintings contain 12% of the original carbon-14, we can set \(\frac{A}{A0} = 0.12\). We can then solve for \(t\) in the equation \(0.12 = e^{-0.000121t}\).

Step 3 ：Solving the equation gives \(t = 17523\).

Step 4 ：Final Answer: The paintings are approximately \(\boxed{17523}\) years old.