Compute the atmospheric pressure at an altitude of $5000m$ if the pressure at sea level is $101\mathrm{.}3$kPa and the $T=15C$ by the following methods:

a$)$ assume air of constant density $=1\mathrm{.}24k\frac{g}{m^3}$

b$)$ assuming that the density of air changes with altitude, but temperature remains constant.