A tracer study is performed using rhodamine $($a fluorescent dye$)$ as a conservative tracer that can

be measured at very low concentrations. The reactor has a volume of $1$ million gallons, and the

wastewater flows through the reactor at $4$ million gallons per day. Determine the rhodamine

concentration in the effluent $6$ hours after the rhodamine is added for the following two

scenarios:

Rhodamine is added to the reactor as a "pulse" input, such that the concentration in the

reactor is $1m\frac{g}{L}$ at time zero. The rhodamine concentration in the influent is zero after time

zero.

Rhodamine is added to the influent as a "step input" such that the influent concentration is

zero before time zero and is $1m\frac{g}{L}$ after time zero. The rhodamine concentration within the

reactor is zero before time zero.