Solution: As $ x o \infty $, $ e^{-0.5x} o 0 $, so $ P(x) o rac{100}{1 + 0} = 100 $. As $ x o -\infty $, $ e^{-0.5x} o \infty $, so $ P(x) o 0 $. The range is $ (0, 100) $. oxed{(0, 100)}