Atmospheric pressure is 14.7 pounds per square inch (lb/in.2) at sea level. An increase in altitude of 1 mi produces a 20% decrease in the atmospheric pressure. Mountain climbers use this relationship to determine whether or not they can safely climb a mountain and to periodically calculate their altitude after they begin climbing.
a. Write a recursive formula that generates a sequence that represents the atmospheric pressure at different altitudes. These mountaineers climbed to an altitude of 11,522 feet to reach the top of Mt. Clark in Yosemite National Park, California.
b. Sketch a graph that shows the relationship between altitude and atmospheric pressure.
c. What is the atmospheric pressure when the altitude is 7 mi?
d. At what altitude does the atmospheric pressure drop below 1.5 lb/in.2?