An $80$ kg man with an aqueous volume of $50$ L is on kidney dialysis to remove built$-$up

urea. The $$kidney dialysis$$ machine removes urea with a rate constant of $0\mathrm{.}6/$hr$.$

A$.$ Write a differential equation for the rate of reduction in urea concentration $($mmol$/$L$/$min$)$

and a differential equation for the rate of removal of urea $($mmol$/$min$).$

B$.$ The man arrives with a blood urea concentration of $20$ millimoles$/$L$.$ What is the initial

instantaneous rate of removal $($in mmol$/$min$)?$

C$.$ How long must he be on dialysis for the urea concentration to drop to $2$ mmol$/$L$?$

D$.$ At this time, what is the final instantaneous rate of removal $($in mmol$/$min$)?$