SNR relation with modulation index and noise power What is the relation between the AM modulation index and the SNR? (I plotted this and it came as the shape of the exponential graph)

Also what is the relation between the channel noise power and the SNR? 
I plotted this and  I got the shape as this graph:



(ignore the labels of the axis)
If $x(t)$ is your message signal, then you can write the AM signal as

$$s(t)=A[1+mx(t)]\cos\omega_0 t$$

where $A&gt;0$ is a real-valued constant, $m$ is the modulation index, and $\omega_0$ is the carrier frequency (in radians). If you assume that the noise added by the channel is white with power spectral density $N_0$, then the SNR after demodulation is

$$SNR=\frac{A^2m^2\overline{x^2(t)}}{4N_0B_x}$$

where $B_x$ is the bandwidth of the message $x(t)$ and $\overline{x^2(t)}$ is its average power.