Mathematics

Problem

A reservoir holds a chemical whose volume remains constant. Let

R_{\text{in}}(t)

and

R_{\text{out}}(t)

denote the inflow and outflow rates (in L/h) of the chemical at time

t

hours, respectively. Describe the condition on

R_{\text{in}}(t)

and

R_{\text{out}}(t)

that guarantees the amount of chemical in the reservoir is decreasing for all

t