$29.$ A $400-$ft equal$-$tangent sag vertical curve has its PVC at station $100+00$ and elevation $500$ ft$.$ The initial grade is $-4\mathrm{.}0\%$ and the final grade is $+2\mathrm{.}5\%.$ Determine the elevation of the lowest point of the curve.

a$.495\mathrm{.}077$ ft

b$.495\mathrm{.}250$ ft

c$.485\mathrm{.}231$ ft

d$.492\mathrm{.}043$ ft