When the substrate concentration $S$ greatly exceeds the saturation constant $K_S$ (i.e. $S \gg K_S$), the Monod equation simplifies: $\mu = \mu_{max} \cdot \dfrac{S}{K_S + S} \approx \mu_{max} \cdot \dfrac{S}{S} = \mu_{max}$. The organism grows at its maximum specific growth rate. Conversely, $K_S$ is numerically equal to the substrate concentration at which $\mu = \mu_{max}/2$.