Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (c)/Statement

Suppose a chemical is being converted to a product in tank. The amount of the chemical is $S$, which is nonnegative and changes with respect to time. If the chemical is being added to the tank at a constant nonnegative rate $R$, then the amount of the chemical in the tank satisfies the differential equation $$\frac{dS}{dt}=R-\frac{S}{2+S}.$$ Describe in words what happens to the amount of the chemical in the tank over a long period of time if $0<R<1$. Support your argument with a phase diagram.