Thermodynamics problem: You have a chemical that accumulates in blood and is excreted at a fixed rate. A man with a total blood volume of 5.5 liters and no initial chemical concentration in his blood is exposed to this chemical at a rate of ke = 90 ng/day. The chemical is excreted at a rate of 0.2 ng/day. There is additional loss of this chemical due to the metabolism in the body. Derive and simplify the differential mass balance equation for this system, and use it to determine how long it will take for the concentration of the chemical in the blood to reach 80 ng/L.

dM/dt = ?

(We assume that the chemical will only accumulate in the blood, so we do not consider the volume of other tissues and organs)

Please explain your answer. thank you