3
\includegraphics[max width=\textwidth, alt={}, center]{68f4b2dc-a05d-4061-aaf0-de15cfe186a9-04_714_515_262_804} The variables \(x\) and \(y\) satisfy the equation \(y = A x ^ { k }\), where \(A\) and \(k\) are constants. The graph of \(\ln y\) against \(\ln x\) is a straight line passing through the points ( \(0.56,2.87\) ) and ( \(0.81,3.47\) ), as shown in the diagram. Find the value of \(k\), and the value of \(A\) correct to 2 significant figures.