You are given a sensor which can be modeled as a first-order system. The input to this sensor (the measurand) is a constant applied at t = 0. The constant input is represented by the variable C for t > 0. The initial reading of the sensor (at t = 0) is represented by the variable yi. Note; yi < C. The time constant of the sensor is given by the variable τ. Required:
Determine an expression for the 90% response time of this system.