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\includegraphics[max width=\textwidth, alt={}, center]{a1f4ccbd-f5ed-437a-ae76-c4925ce86e25-05_538_531_264_246}
The shape \(A B C\) shown in the diagram is a student's design for the sail of a small boat.
The curve \(A C\) has equation \(y = 2 \log _ { 2 } x\) and the curve \(B C\) has equation \(y = \log _ { 2 } \left( x - \frac { 3 } { 2 } \right) + 3\).
- State the \(x\)-coordinate of point \(A\).
- Determine the \(x\)-coordinate of point \(B\).
- By solving an equation involving logarithms, show that the \(x\)-coordinate of point \(C\) is 2 .
It is given that, correct to 3 significant figures, the area of the sail is 0.656 units \(^ { 2 }\).
- Calculate by how much the area is over-estimated or under-estimated when the curved edges of the sail are modelled as straight lines.