When the air temperature reaches the dew point, fog may form. This phenomenon also causes clouds to form at higher altitudes. Both the air temperature and the dew point decrease at a constant rate as the altitude above ground level increases. If the ground-level
temperature and dew point are To and Do, respectively, the air temperature at an altitude of x miles can be approximated by
T(x) = To - 19x, and the dew point can be approximated by D(x) = D.-5.8x. Suppose the ground-level temperature is 65°F and the dew
point is 50°F. Note that clouds will not form at altitudes for which the air temperature is above the dew point.
(a) Use the intersection-of-graphs method to estimate the altitudes at which clouds will not form.
(b) Solve part (a) analytically.
TORRE