A key requirement for using memristors in circuits is a predictive model for device behavior that can be used in simulations and to guide designs. We analyze one of the most promising materials, tantalum oxide, for high density, low power, and high-speed memory. We perform an ensemble of measurements, including time dynamics across nine decades, to deduce the underlying state equations describing the switching in Pt/TaO x /Ta memristors. A predictive, compact model is found in good agreement with the measured data. The resulting model, compatible with SPICE, is then used to understand trends in terms of switching times and energy consumption, which in turn are important for choosing device operating points and handling interactions with other circuit elements.