A lagoon treatment system with a volume $1,200$ m has been receiving a steady flow of a non$-$conservative waste at a rate of $100$ m$?/$day for a long enough time a steady flow c steady$-$state conditions apply. The waste has a $1$s order decay rate of $0\mathrm{.}2/$day and enters the lagoon at a concentration of $10$ mg$/$L$.$ Assume completely mixed.$($a$)$ What would be the concentration of pollutant in the effluent leaving the lagoon?$($b$)$ If the input waste concentration suddenly increased to $100$ mg$/$L$,$ what would the concentration in the effluent be $7$ days later?