We present and analyze the room temperature (T= 23.5 degrees C) time behavior of the transmitted intensities of polarized light passing through an unclamped (100)-type single crystal of barium titanate (BaTiO3) when subject to a time-dependent, externally applied electric field. To the authors' knowledge, this is the first reported observation and analysis of such time-resolved optical transients. According to a previous [J. Opt. Soc. Am. A 22, 377 (2005)] observation by the authors, this original optical technique can, in principle, be used on 18 out of 20 noncentrosymmetric crystal point groups where the first-order (Pockels) and second-order (Kerr) electrooptic effects coexist. Because of its nondestructive nature, this novel optical method would be a useful tool in other fields of condensed-matter physics in which time-behavior observation and characterization of certain physical parameters of crystals are important.