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Time-resolved measurements of the ionization states of warm dense aluminum via K-shell absorption spectroscopy are demonstrated using betatron radiation generated from laser wakefield acceleration as a probe. The warm dense aluminum is generated by irradiating a free-standing nanofoil with a femtosecond optical laser pulse and was heated to an electron temperature of ~20-25 eV at a close-to-solid mass density. Absorption dips in the transmitted x-ray spectrum due to the Al4+ and Al5+ ions are clearly seen during the experiments. The measured absorption spectra are compared to simulations with various ionization potential depression models, including the commonly used Stewart-Pyatt model and an alternative modified Ecker-Kröll model. The observed absorption spectra are in approximate agreement with these models, though indicating a slightly higher state of ionization and closer agreement for simulations with the modified Ecker-Kröll model. [ABSTRACT FROM AUTHOR]