One Kilogram of a contaminant is spilled at a point in a $4-$meter$-$deep reservoir and is instantaneously mixed over the entire depth.

$($a$)$ If the Diffusion coefficients in the N$-$S & E$-$W Direction are $5\frac{m^2}{s}$ and $10\frac{m^2}{s}$ respectively, calculate the concentration as a function of time at location $100$ meters North and $100$ meters East of the spill.

$2\mathrm{.}8135\frac{{10}^{-3}}{t}{e}^{-(\frac{187\mathrm{.}5}{t})}$

$($b$)$ What is the concentration at the spill location after $5$ minutes?