Problem $2(10$ points$)$:

For what value of $$ is the following approximation valid:

erfc$[]1-\frac{2}{\sqrt[\phantom{2}]{}}$

within an error of: $($a$)5$ percent, and $($b$)$ within $1$ percent?

Problem $1(15$ points$)$:

A landfill is leaking leachate with chloride concentration $c_0=725m\frac{g}{L},$ which enters an aquifer with hydraulic conductivity of $0\mathrm{.}003c\frac{m}{s},-d\frac{h}{d}x=0\mathrm{.}002,$ porosity $=0\mathrm{.}23,$ and hydrodynamic dispersion coefficient of $3\mathrm{.}91{10}^{-7}\frac{m^2}{s}.$ Assuming that the transport of chloride in the aquifer can be described by the following expression:

$c(x,t)=\frac{c_0}{2}$erfc$[\frac{x-Ut}{2(D_{x}t{)}^{\frac{1}{2}}}]+\frac{1}{2}$exp$[\frac{Ux}{D_x}]$ erfc $\frac{x+Ut}{2(D_{x}t{)}^{\frac{1}{2}}}$

Compute the concentration of chloride in one year at a distance $15$ meters from the point where the leachate entered the groundwater.