1. Several recent expeditions climbing Mount Everest have had physiologists who are trying to learn about human physiology under extreme conditions. Mount Everest stresses the human body because of the harsh conditions, but primarily because of the very thin air. The high elevation results in low O₂ availability. This causes increased ventilation rates of 5 to 6 fold, which results in alkaline blood. You can read more about this on PBS Nova webpage:

a. The atmospheric pressure p (in mm Hg) as a function of elevation (in feet), x, that satisfies the differential equation:

where k is a constant and p₀ = 760 mm Hg. In 1981, Christopher Pizzo took a barometer to the top of Mount Everest (29,028 ft) and found the pressure to be 253 mm Hg. Use this information to solve the differential equation above and find the constant k (to 4 significant figures). What are the units on k? Graph the solution for x [0, 30000].

b. Find the barometric pressure at 1 mile (5,280 ft) and on top of Mount Whitney (14,494 ft). Without prior conditioning, few people can survive when the pressure drops to less than 380 mm Hg. How high is this?