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\includegraphics[max width=\textwidth, alt={}, center]{4d03f4e3-ae6c-4a0d-ae4d-d89258d2919a-4_417_931_255_607}
The diagram shows the curve \(y = 2 ^ { x } - 3\).
- Describe the geometrical transformation that transforms the curve \(y = 2 ^ { x }\) to the curve \(y = 2 ^ { x } - 3\).
- State the \(y\)-coordinate of the point where the curve \(y = 2 ^ { x } - 3\) crosses the \(y\)-axis.
- Find the \(x\)-coordinate of the point where the curve \(y = 2 ^ { x } - 3\) crosses the \(x\)-axis, giving your answer in the form \(\log _ { a } b\).
- The curve \(y = 2 ^ { x } - 3\) passes through the point ( \(p , 62\) ). Use logarithms to find the value of \(p\), correct to 3 significant figures.
- Use the trapezium rule, with 2 strips each of width 0.5 , to find an estimate for \(\int _ { 3 } ^ { 4 } \left( 2 ^ { x } - 3 \right) \mathrm { d } x\). Give your answer correct to 3 significant figures.