The altitude of an airplane is calculated by measuring atmospheric pressure on the surface of the airplane. This pressure is exponentially related to the plane's height above Earth's surface. At ground level, the pressure is 14.7 pounds per square inch (abbreviated lb/in.2, or psi). At an altitude of 2 mi, the pressure is reduced to 9.46 lb/in.2.
a. Write an exponential equation for altitude in miles as a function of air pressure.
b. Sketch the graph of air pressure as a function of altitude. Sketch the graph of altitude as a function of air pressure. Graph your equation from 9a and its inverse to check your sketches.
c. What is the pressure at an altitude of 12,000 ft? (1 mi = 5280 ft)
d. What is the altitude of an airplane if the atmospheric pressure is 3.65 lb/in.2?