Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (b)/Solution 1

For all $S\ge 0$, $\frac{S}{2+S}<1$. Since $\frac{3}{2}>1$, we have that $$\frac{3}{2}-\frac{S}{2+S}>\frac{3}{2}-1>0,$$ so $\frac{dS}{dt}>0$ for all nonnegative $S$. That is, over time the substrate builds up without bound.