Goodbyes are intrinsically designed to be an exponential (or maybe logarithmic?). It starts from a sentence length fitting to the warmth of the relationship, and then each statement is cut shorter and shorter until you reach the a-tom, the uncuttable unit, and then it the goodbye collapses to zero.
Allow me to demonstrate with a short scene:
Warm friend A: "Oh, gosh, look at the time? I really ought to be heading in the direction of work -- I've been late lately, so I should get going."
Warm friend B: "Oh yeah, it is late, isn't it. I hope you make it to work on time."
Warm friend A: "I hope so too. Good luck with your presentation tomorrow!"
Warm friend B: "Thanks! I'll see you soon!"
Warm friend A: "Okay, then -- bye!"
Warm friend B: "Bye!"
Conversation is now concluded.
If you don't observe this decay, it feels a little abrupt. Observe:
Warm friend A: "Oh, gosh, look at the time? I really ought to be heading in the direction of work -- I've been late lately, so I should get going."
Warm friend B: "Bye."
Conversation is now concluded.
I know some people who exploit this to make it impossible to get off the phone with them -- because if at any moment you reverse the decay, you are basically starting the goodbye over again.
My God I've cracked the code!
