Complete the table shown to the right for the population growth model for a certain country.
\begin{tabular}{|c|c|c|}
\hline \begin{tabular}{c}
2004 \\
Population (millions)
\end{tabular} & \begin{tabular}{c}
Projected 2037 \\
Population (millions)
\end{tabular} & \begin{tabular}{c}
Projected \\
Growth Rate, $\mathbf{k}$
\end{tabular} \\
\hline 56.3 & 36.6 & \\
\hline
\end{tabular}

Step 1 ：Given the population growth model is represented by the equation \(P = P_0 \cdot e^{kt}\), where \(P\) is the final population, \(P_0\) is the initial population, \(k\) is the growth rate, and \(t\) is the time in years.

Step 2 ：For this problem, we know \(P = 36.6\) million, \(P_0 = 56.3\) million, and \(t = 2037 - 2004 = 33\) years. We need to find \(k\).

Step 3 ：We can rearrange the equation to solve for \(k\): \(k = \frac{ln(P/P_0)}{t}\).

Step 4 ：Substituting the given values into the equation, we get \(k = \frac{ln(36.6/56.3)}{33}\).

Step 5 ：Solving the equation, we find that \(k = -0.01304988771934315\).

Step 6 ：Rounding to three decimal places, the projected growth rate, \(k\), is \(\boxed{-0.013}\).