$22.$ In order to apply state plane coordinates, a distance measured at an elevation of $4000$ ft has been reduced to sea level. If the distance is $2\mathrm{.}5$ mi when reduced to sea level and the earth has a radius of $20,906,000$ ft$,$ what is the distance at $4000$ ft$?$

$($A$)13,197\mathrm{.}47$ ft

$($B$)13,200\mathrm{.}00$ ft

$($C$)13,202$:$53$ ft

$($D$)13,204\mathrm{.}12$ ft