Resonant slow extraction is used to provide an intense quasi-DC flux of high-energy protons for the Fixed Target (FT) physics programme at the CERN Super Proton Synchrotron (SPS). The unavoidable beam loss intrinsic to the extraction process activates the extraction region and its equipment. Although the radiation dose to equipment has an impact on availability, the cool-down times required to limit dose to the personnel carrying-out maintenance of the accelerator also pose important restrictions, and ultimately limit the number of protons on target. In order to understand how the extracted proton flux affects the build-up and subsequent cool-down of the induced activation, a model based on a simple empirical relationship has been developed and shown to predict the measured radioactive decay at ionisation chambers located along the extraction region. In this contribution, the empirical model is described, its strengths and limitations discussed, and its application as a predictive tool for estimating cool-down times as a function of extracted proton flux demonstrated