5 It is given that \(\int _ { 0 } ^ { p } 4 x \mathrm { e } ^ { - \frac { 1 } { 2 } x } \mathrm {~d} x = 9\), where \(p\) is a positive constant.
- Show that \(p = 2 \ln \left( \frac { 8 p + 16 } { 7 } \right)\).
- Use an iterative process based on the equation in part (i) to find the value of \(p\) correct to 3 significant figures. Use a starting value of 3.5 and give the result of each iteration to 5 significant figures.