Step 1: Understanding Michaelis-Menten Kinetics
The Michaelis-Menten reaction describes enzyme kinetics where the reaction order changes with substrate concentration. Initially, it follows first-order kinetics at low substrate concentrations and zero-order kinetics at high substrate concentrations.
Step 2: Conclusion
As the order of the reaction varies with the concentration of the substrate, it is classified as a "changing order" reaction.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.