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The variables \(x\) and \(y\) satisfy the equation \(y = 4 ^ { 2 x - a }\), where \(a\) is an integer. As shown in the diagram, the graph of \(\ln y\) against \(x\) is a straight line passing through the point \(( 0 , - 20.8 )\), where the second coordinate is given correct to 3 significant figures.
- Show that the gradient of the straight line is \(\ln 16\).
- Determine the value of \(a\).