Amorphous oxide semiconductors (AOS) are promising candidate materials for thin film transistors in display devices, but one major challenge for mass application is their instability under illumination. In this work, a theoretical method for analyzing transient photoconductivity response in such AOS thin films is reviewed, namely the continuous multi-exponential model. This model can deduce a continuous distribution of decay time constants representing activation energy levels in an AOS, and is shown to reliably reproduce a model of density of states (DOS) of mid-gap traps assumed to be responsible for the transient photoconductivity. Provided the data collection time is sufficiently long, the continuous multi-exponential model was verified to reconstruct the modeled continuous DOS spectrum, thus providing a powerful tool to analyze photoresponse in AOS. This method has the advantage that no prior assumptions about the form of the density of states are needed, but the drawback that long data collection times are required for the transient to be fully relaxed.