A radioactive substance decays according to the following function, where $y_{0}$ is the initial amount present, and $y$ is the amount present at time $t$ (in days).
\[
y=y_{0} e^{-0.019 t}
\]
Find the half-life of this substance. Do not round any intermediate computations, and round your answer to the nearest tenth.
days

Step 1 ：We are given a radioactive substance that decays according to the function \(y=y_{0} e^{-0.019 t}\), where \(y_{0}\) is the initial amount present, and \(y\) is the amount present at time \(t\) (in days).

Step 2 ：We are asked to find the half-life of this substance. The half-life of a substance is the time it takes for half of the substance to decay. In other words, it's the time \(t\) when \(y = \frac{y_0}{2}\).

Step 3 ：We can set up the equation \(\frac{y_0}{2} = y_0 e^{-0.019 t}\) and solve for \(t\).

Step 4 ：Let's set \(y_0 = 1\) and \(y = 0.5\).

Step 5 ：Solving the equation gives us \(t = 36.481430555786595\).

Step 6 ：Rounding to the nearest tenth, we get \(t = 36.5\) days.

Step 7 ：Final Answer: The half-life of the substance is approximately \(\boxed{36.5}\) days.