Complete the table shown to the right for the half-life of a certain radioactive substance.
\begin{tabular}{|l|l|}
\hline Half-Life & Decay Rate, $\mathbf{k}$ \\
\hline & $4.9 \%$ per year $=-0.049$ \\
\hline
\end{tabular}

Step 1 ：We are given a table with the decay rate, \(k\), of a certain radioactive substance. The decay rate is given as \(4.9\%\) per year, which is equivalent to \(-0.049\) per year.

Step 2 ：The half-life of a radioactive substance is the time it takes for half of the substance to decay. The relationship between the half-life (t) and the decay rate (k) is given by the formula: \(t = \frac{ln(2)}{|k|}\), where ln is the natural logarithm.

Step 3 ：We can substitute the given decay rate into the formula to find the half-life. Let's substitute \(k = -0.049\) into the formula.

Step 4 ：After substituting, we get \(t = \frac{ln(2)}{|-0.049|}\).

Step 5 ：Solving the equation gives us \(t \approx 14.145860827753985\).

Step 6 ：So, the half-life of the radioactive substance is approximately \(\boxed{14.15}\) years.