The intensity of a light pulse travelling along a communication channel decreases exponentially with distance x according to the relation `I=I_(0)e^(-alphax)`, where `I_(0)` is the intensity at x = 0 and `alpha` is the attenuation constant.
(a) Show that the intensity reduces by `75%` after a distance of `((ln4)/(alpha))`.
(b) Attenuation of a signal can be expressed in decibel (dB) according to the relation dB = `10 log _(10)((I)/(I_(0)))`. What is the attenuation in dB/km for an optical fibre in which the intensity falls by 50% over a distance of 50 km?