Find the half-life of a radioactive element, which decays according to the function $A(t)=A_{0} e^{-0.022 t}$, where $t$ is the time in years.

Step 1 ：We are given the decay function of a radioactive element as \(A(t)=A_{0} e^{-0.022 t}\), where \(t\) is the time in years and \(A_{0}\) is the initial amount of the substance.

Step 2 ：The half-life of a radioactive element is the time it takes for half of the atoms in a sample to decay. In other words, it's the time at which the amount of the substance is half its initial amount. So, we need to find the time \(t\) when \(A(t) = \frac{1}{2}A_{0}\).

Step 3 ：We set up the equation \(A_{0} e^{-0.022 t} = \frac{1}{2}A_{0}\).

Step 4 ：Solving this equation gives us the half-life of the radioactive element.

Step 5 ：Final Answer: The half-life of the radioactive element is approximately \(\boxed{31.51}\) years.