Under normal conditions the temperature of the atmosphere decreases with increasing elevation. In some situations, however, a temperature inversion may exist so that the air temperature increases with elevation. A series of temperature probes on a mountain give the elevation temperature data shown in the table below. If the barometric pressure at the base of the mountain is 12.1 psia, determine by means of numerical integration the pressure at the top of the mountain.

Elevation (ft) Temperature (F) 5000 5500 6000 6400 7100 7400 8200 8600 9200 9900 50.1 (base) 55.2 60.3 62.6 67.0 68.4 70.0 69.5 68.0 67.1 (top)