What is the relation between Freq vs Distance AND BW v Dist

Can anyone point me to the formula that relates the following:

Formula for Freq vs Distance

Formula for Freq vs Bandwidth

In a link budget communication link analysis distance is related to frequency and to the free-space path loss. Lower the frequency and smaller path loss, greater the distance.

Also from the link budget if you know the transmitted power, antenna gain, path loss, cable loss, etc, you can get the required receiver sensitivity for a specific SNR.

Receiver sensitivity is related to the bandwidth of the system. Narrower the bandwidth, better sensitivity.

Link budget analysis is also highly dependent on the environment you're analyzing. HF over the horizon propagation is very different from satellite LOS communication. Lots of empirical models and very few analytical formulas are available.