Digital devices are ubiquitous in modern society. Every action on a digital device, whether initiated by a user, an application, the operating system, or hardware, leaves behind evidence of the activity in the form of digital artifacts such as files, memory content, and network traffic. Such artifacts are used by digital forensics investigators to reconstruct past activity, and by criminals seeking to harvest private or sensitive information. The persistence of an artifact over time directly affects its ability to be recovered at a later date, yet a rigorous, comprehensive theory of digital artifact persistence does not exist. This research proposes and demonstrates a method to facilitate the studies necessary to develop such a theory. We implemented a differential analysis approach in which sequential digital media images are analyzed for deleted file persistence. The contents of files deleted between the first two images are tracked in the remaining images. This data forms a decay curve for each file over time and activity. Since we also have access to system and storage media properties, deleted file properties, and the details of actions taken between images, we can begin to form testable hypotheses about the factors affecting deleted file persistence. We have implemented prototype software to conduct this analysis, and we demonstrate the method on images generated in a controlled environment as well as on a series of realistic system images.