The persistent organic pollutant, polychlorinated biphenyls $($PCBs$),$ is a common contaminant in groundwater.

Suppose a municipal drinking water supply has an average PCBs concentration of $\backslash (10\backslash$mu $\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$L$\}\backslash ).$ The toxicity data for PCBs are:

Slope factor $($potency$),$ oral route $\backslash (=7\mathrm{.}7(\backslash$mathrm$\{$mg$\}/\backslash$mathrm$\{$kg$\}/\backslash$text $\{$ day $\})^\{-1\}\backslash )$

$\backslash (\backslash$mathrm$\{$RfD$\}=0\mathrm{.}0001\backslash$mathrm$\{$mg$\}/\backslash$mathrm$\{$kg$\}/\backslash )$ day

Assumptions:

i$)$ Daily water consumption rate for an adult is $\backslash (2\backslash$mathrm$\{$~L$\}/\backslash )$ day

ii$)$ Body weight of an adult is $70$ kg

iii$)$ Lifetime is $70$ years

iv$)$ Absorption factor is $1$

v$)$ Residents go out of town for one week each year

$($a$)$ Estimate the lifetime risk of cancer for an adult associated with drinking the water that is contaminated with PCBs$.$

$($b$)$ If this drinking water supply serves a city of $400,000$ people, what number of extra cancers per year would be expected?

$($c$)$ Define the term Hazard Quotient. Determine whether there is any non$-$carcinogenic risk in drinking the PCB contaminated water.

$($d$)$ At what level should the PCBs concentration be reduced to in order to allow for safe human consumption if the lifetime acceptable risk for cancer is $\backslash (1\backslash$times $10^\{-6\}\backslash ).$

$($e$)$ Aside from exposure due to drinking the contaminated water, comment on exposure to the contaminated water via other exposure pathways.

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