The amount of carbon-14 present in animal bones after $t$ years is given by $P(t)=P_{0} e^{-0.00012097 t} \cdot A$ bone has lost $23 \%$ of its carbon-14. How old is the bone?

Step 1 ：The problem is asking for the age of the bone, given that it has lost 23% of its carbon-14. This means that the bone has 77% (100% - 23%) of its original carbon-14 left.

Step 2 ：We can set up the equation \(P(t) = 0.77P_{0}\) and solve for \(t\).

Step 3 ：Let \(P0 = 1\), \(P_t = 0.77\), and \(k = -0.00012097\).

Step 4 ：Solving the equation gives \(t = 2160.5750527767837\).

Step 5 ：Rounding to the nearest whole number, the final answer is \(\boxed{2161}\) years old.