Model when Substrate is Inhibitory

where µ = specific growth rate coefficient (the hat denotes its maximum value)
k_s = half-saturation coefficient
k_i = inhibition coefficient
S = concentration of inhibitory nutrient

Note that the inhibition coefficient, K_i, is in the denominator multiplied by the substrate concentration squared. This term dominates as S gets large and causes µ to decline.

Reference

• MuVsS.ms - Maple Program to Draw Graphs