If the elevation equation for a vertical curve is as shown below, find the elevation at station $20+00$ in foot. Consider the PVC station as $15+00.$

Curve Elevation Equation $=-0\mathrm{.}316x^2+5x+45$

a$)77\mathrm{.}90$

b$)12\mathrm{.}10$

c$)62\mathrm{.}10$

d$)55\mathrm{.}53$

e$)42\mathrm{.}10$