As mentioned in the discussion of the law of atmospheres, the fractional decrease in atmospheric pressure is proportional to the change in altitude. Expressed in mathematical terms we have where C is a constant.

(a) Show that P(h) = P0 e-Ch is a solution of the differential equation.

(b) Show that if ∆h << h0, then P(h + ∆h) » P(h) (1 – ∆h/h0), where h0 = 1/C.

(c) Given that the pressure at h = 5.5 km is half that at sea level, find the constant C.