$\backslash$table$[[$Elevation $($ft$),$Temperature $(F)],[5000,50\mathrm{.}1($base$)],[5500,55\mathrm{.}2],[6000,60\mathrm{.}3],[6400,62\mathrm{.}6],[7100,67\mathrm{.}0],[7400,68\mathrm{.}4],[8200,70\mathrm{.}0],[8600,69\mathrm{.}5],[9200,68\mathrm{.}0],[9900,67\mathrm{.}1($top$)]]$

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. If the barometric pressure at the base of the mountain is $12\mathrm{.}1$ psia, determine by means of numerical integration the pressure at the top of the mountain.