(i) 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.
Show that the intensity reduces by 75 percent after a distance of `(ln 4)/(alpha)`
(ii) Attenuation of a signal can be expressed in decibel (dB) according to the relation
dB `= 10log_10 (I//I_0).` What is the attenuation in `dB//km` for an optical fibre in which the intensity falls by 50 percent over a distance of 50 km?
A. 0.7
B. 0.75
C. 0.8
D. 0.85
