Air pressure at sea level is 30 inches of mercury. At an altitude of h feet above sea level, the air pressure, P, in inches of mercury, is given by
(a) Sketch a graph of P against h.
(b) Find the equation of the tangent line at h = 0.
(c) A rule of thumb used by travelers is that air pressure drops about 1 inch for every 1000-foot increase in height above sea level. Write a formula for the air pressure given by this rule of thumb.
(d) What is the relation between your answers to parts (b) and (c)? Explain why the rule of thumb works. (e) Are the predictions made by the rule of thumb too large or too small? Why?