The answer will vary significantly with the construction of the home or room in question. The amount and rating of insulation, AC system type and efficiency, the volume of external air that is exchanged with the inside (which is substantial), windspeed, angle of the sun, potential shade, the existence of internal heat sinks (such as a large basement) must all be considered. Every variable could drastically change the slope and form of the overall function of heat pump input energy as it relates to exterior air temperature.
The percentage of surface area exposed to the external heat is likely the most significant variable. A perfect 6-sided cube of a home, for instance, would have 5/6th of its surface area exposed to heat. The bottom of the cube, as it's against the ground with a different temperature, may act as a sink. On other hand, a squashed rambler may have a much larger roof area that could, in extreme cases, mean just under 1/2 of the total surface area is exposed to the heat, in relation to the potential basement/floor sink.
The ability of the AC condenser unit to release its absorbed heat is a massive factor contributing to energy use per BTU. A clogged fan or debris around the condenser could ruin efficiency, especially at high duty cycle.
Long story short, you cannot take such a tremendously dynamic system and simplify it in a way that would reasonably apply to an imaginary situation. The only basic concepts you could rely upon are conservation of energy and Newton's 2nd law.