On Earth, the atmospheric pressure, p, in bars can be modelled approximately by the formula p = e^−0.13h where h is the height above sea level in kilometres.

a. Use this model to estimate the pressure at the top of Mount Rainier, which has an altitude of 4.394 km.

b. Demonstrate that dp/dh = kp where k is a constant to be found.

c. Interpret the significance of the sign of k in part b.

d. This model predicts that the atmospheric pressure will change by s% for every kilometre gained in height. Calculate the value of s.