For amplitude modulation, the amplitude of the carrier wave is modified. We add the signal to the amplitude of the carries wave.

Suppose that the carrier wave is given by;

and the signal is given by:

We will add this signal to amplitude of carrier wave (A_c) to get the amplitude of the modulated wave. The modulated wave is given by replacing the old amplitude by the new one in the equation for the carrier wave. The expression for the modulated wave found is the same one as given in (c).