Aqueous solutions of half-ionized tetradecyldimethylamine oxide (TDAO) with 0.1 M NaCl and varying surfactant concentration were studied by small-angle neutron scattering. The scattering data demonstrate the presence of wormlike micelles, and an analysis based on polymer theory and the results from Monte Carlo simulations was performed. The surfactant concentrations correspond to dilute and semidilute solutions for the wormlike micelles. The analysis of the forward scattering demonstrates a concentration dependence of the growth of the micelles in agreement with mean-field theory. The scattering data in the full range of measured scattering vectors were analyzed using a modified random phase approximation expression, and excellent agreement was found for concentrations up to 65 times the overlap concentration. The model fitting showed that the micelles have an elliptical cross section with semiaxes of about 16 and 28 Angstrom. Based on the self-consistent analysis, an independent comparison between the correlation length determined from the scattering data and from Monte Carlo simulations was performed as a function of the reduced concentration.