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A bleaching model describing the dynamics of Hill grating formation in optical fibers, [K.O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978)], is analytically solved in an undepleted pump approximation. This regime provides quantitative predictions about grating dynamics in the early stages of grating growth. A series of experiments in which heating effects and surface reflections from the input end of the fiber have been eliminated show quantitative agreement with the theory to 2%.