assuming that the atomspher is locally isothermal, the air density variation with pressure is giving by B=B0*(P/P0) where B is density ,p is pressure , and the subscript 0 denotes conditions at the earth's surface.

show that the pressure variation through the isothermal atomspher is: B/B=exp(-P0gz/P0) where z is the hight above the surface of the earth and g is the acceleration of gravity (assumed constant).