Problem $3$: A water supply source contains $0\mathrm{.}5m\frac{g}{L}$ of a chemical $x$ that is known for its carcinogenic and non$-$carcinogenic effects. For a $70-kg$ person who drinks $1\mathrm{.}5\frac{L}{d}$ of this water for $10$ years, and assuming that this chemical has a potency factor of $0\mathrm{.}02(m\frac{g}{k}g.d{)}^{-}$and a reference dose of $0\mathrm{.}35m\frac{g}{k}g.$d:

a$)$ What is the incremental lifetime cancer risk of consuming this water?

b$)$ What is the non$-$cancer risk $($hazard index$)?$

c$)$ Assume that a lake is polluted with $0\mathrm{.}5m\frac{g}{L}$ of the same chemical $x,$ and a person consumes $200g$ of fish every month, for $12$ months per year and for a total of $10$ years. What is the incremental lifetime cancer risk of consuming fish from this lake given that the bioconcentration factor is $8\mathrm{.}2\frac{L}{k}g?$