Amplitude Modulation Circuit Implementation
If \$V_{G2}(t)\$ is a carrier sine wave, then you can start the analysis by setting the audio voltage to zero. You'll find that the output is equal to \$G\cdot V_{G2}(t)\$, assuming operation in the linear region of the transistor.

In the calculation of the gain \$G\$, you'll find that it depends on the emitter current. Now let the audio voltage increase; this produces a reduction in the emitter current and a correponding reduction in the gain. If the audio voltage is negative, the emitter current increases, and the gain increases.

In other words, the audio voltage controls the amplitude of the carrier, and this is what defines amplitude modulation.