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 $\mathbf{1 1 . 5}$ days & \\ \hline \end{tabular} \[ k=\square \] (Round to six decimal places as needed.) Ask my instructor Clear all Check answer

Step 1 ：The decay rate of a radioactive substance is related to its half-life by the formula: \(k = \frac{\ln(2)}{T}\), where \(k\) is the decay constant, \(T\) is the half-life of the substance, and \(\ln\) is the natural logarithm function.

Step 2 ：In this case, the half-life \(T\) is given as 11.5 days. We can substitute this into the formula to find the decay rate \(k\).

Step 3 ：Substituting \(T = 11.5\) into the formula, we get \(k = \frac{\ln(2)}{11.5}\).

Step 4 ：Calculating the above expression, we get \(k = 0.06027366787477785\).

Step 5 ：Rounding to six decimal places, we get \(k = 0.060274\).

Step 6 ：Final Answer: The decay rate, \(k\), for the radioactive substance with a half-life of 11.5 days is approximately \(\boxed{0.060274}\).