How transmitted power is related to modulation index in am?

In amplitude modulation (AM), the modulation index (m) represents the ratio of the peak amplitude of the modulating signal to the peak amplitude of the carrier signal. The transmitted power in an AM signal increases with the modulation index, as higher modulation indices lead to greater variations in the carrier's amplitude. Specifically, the total transmitted power can be expressed as a function of the carrier power and the modulation index, with more power being allocated to sidebands as m increases. However, beyond a certain point, further increasing the modulation index can lead to distortion, as the signal may exceed the linear range of the amplifier.