Specific loudness rises steeply then saturates toward a power-law asymptote

Evidence

As outlined in Fig. 8.17, the specific loudness, N’, rises rapidly for low values of LE. For large values of LE, all curves reach an asymptote, given by the dashed line, which corresponds to the power law with an exponent of 0.23. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1273