Assume that if the temperature is constant, then the atmospheric pressure p varies with the altitude h (above sea level) in such a way that (dp)/(dh) = kp where k is constant. Find a formula for p in terms of k, h, and the atmospheric pressure p0 at sea level. Solution dp/dh = kp dp/p = k dh Integrate: ln(p) = kh + C p = ekh + C at sea level: h = 0 , thus p0 = e0+C --> eC = p0 Therefore: p = ekh + C = eC.ekh = p0 ekh.