The apparent brightness of asteroids is proportional to r ~ 2 * d ~ 2t where rd is the distance of the asteroid from the Sun

The apparent brightness of asteroids is proportional to r ~ 2 * d ~ 2t where rd is the distance of the asteroid from the Sun and the Earth. For comets, the brightness is proportional to r ~ N * d ~ 2, where the number N varies from 4 to 6. What is the reason for this difference?

When approaching the Sun, the ice that is part of the comets evaporates. Together with dust particles, it forms the head and tail of the comet, which significantly improve its ability to reflect sunlight.