Problem $11.(16\mathrm{.}7$ Chin$-$edited$)$ The risk, $\backslash ($ R $\backslash ),$ of illness from viruses in pumped water is related to the viral concentration, $\backslash ($ c $\backslash ),$ where $\backslash ($ c $\backslash )$ is in $\backslash$#$/$L$,$ by the relation

$\backslash [$

R$=1-(1+4\mathrm{.}76$ c$)^\{-94\mathrm{.}9\}$

$\backslash ]$

$($a$)$ If an illness rate of $1$ in $10,000$ people is acceptable $(\backslash (\backslash$boldsymbol$\{$R$\}=\backslash$boldsymbol$\{0.0001\}\backslash )),$ determine the allowable viral concentration in the pumped water.

$($b$)$ A municipal water supply well is to be installed $100$ m from a school that uses a septic tank for on$-$site wastewater disposal. The well is to have a rated capacity of $\backslash (400\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$s$\}\backslash ),$ the saturated thickness of the aquifer is $20$ m $,$ and the porosity of the aquifer is $0\mathrm{.}17.$ If the allowable risk of viral infection from the pumped water is $0\mathrm{.}0001$ and the decay constant for viruses in ground water is $\backslash (0\mathrm{.}3\backslash$mathrm$\{$~d$\}-1\backslash ),$ estimate the maximum allowable virus concentration in the groundwater below the school.