Show that the variation of atmospheric pressure with altitude is given by P = P0e─ay, where a = pog/P0, P0 is atmospheric pressure at some reference level y = 0, and p0 is the atmospheric density at this level. Assume that the decrease in atmospheric pressure over an infinitesimal change in altitude (so that the density is approximately uniform) is given by dP = ─ pg dy, and that the density of air is proportional to the pressure.