Experiments were performed to observe the growth of the turbulent Rayleigh-Taylor unstable mixing layer generated between air and SF6, with an Atwood number of A=(?2-?1)/(?2+?1)=0.64, where ?1 and ?2 are the densities of air and SF6 respectively. A non-constant acceleration with an average value of 2300g0, where g0 is the acceleration due to gravity, was generated by interaction of the interface between the two gases with a rarefaction wave. Three-dimensional multi-mode perturbations were generated on the diffuse interface, with a diffusion layer thickness of d=3.6mm, using a membraneless vertical oscillation technique, and 20 experiments were performed to establish a statistical ensemble. The average perturbation from this ensemble was found and used as input for a numerical simulation using the LLNL Miranda code. Good qualitative agreement between the experiment and simulation was observed, while quantitative agreement was best at early to intermediate times. Several methods were used to extract the turbulent growth constant a from experiments and simulations while accounting for time varying acceleration. Experimental, average bubble and spike asymptotic self-similar growth rate values range from a=0.022 to a=0.032 depending on the method used, and whether or not they account for variable acceleration. Values found from the simulations range from a=0.024 to a=0.041. Values of a measured in the experiments are lower than what are typically measured, but are more in line with those found in recent simulations.