The reason exposure time must be increased by a factor of four when the source-to-film distance is doubled is that the:

Intensity of radiation decreases at an exponential rate when the source-to-film distance is increased

Energy of radiation is inversely proportional to the square root of the distance from the source to the film

Intensity of radiation is inversely proportional to the square of the distance from the source to the film

Scattered radiation effect is greater as the source-to-film distance increases