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.

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