Assume that an AM system operates with an index of 0.5 and that the message signal is 10 cos(8πt). Compute the efficiency, the detection gain in dB, and the output SNR in decibels relative to the base band performance P_T / N₀W. Determine the improvement (in decibels) in the output SNR that results, if the modulation index is increased from 0.5 to 0.8.