The amount of carbon-14 present in animal bones after $t$ years is given by $P(t)=P_{0} e^{-0.00012 t}$. A bone has lost $36 \%$ of its carbon-14. How old is the bone? The bone is about years old. (Round to the nearest integer as needed.)

Step 1 ：The problem is asking for the time $t$ when the amount of carbon-14 in the bone is $64\%$ of the original amount (since it has lost $36\%$). This can be represented by the equation $0.64P_{0}=P_{0} e^{-0.00012 t}$.

Step 2 ：We can solve this equation for $t$ by setting $P_{0} = 1$ and $P = 0.64$.

Step 3 ：Solving the equation gives $t = 3719.0591885701624$.

Step 4 ：Rounding to the nearest integer gives $t = 3719$.

Step 5 ：Final Answer: The bone is approximately \(\boxed{3719}\) years old.