If the temperature in the atmosphere is assumed to vary linearly with altitude so \(T=T_{o}-\alpha z\) where \(T_{o}\) is the sea level temperature and \(\alpha=-d T / d z\) is the temperature lapse rate, find \(p(z)\) when air is taken to be a perfect gas. Give the answer in terms of \(p_{o}, \alpha, g, R\) and \(z\) only.