We describe a new statistical model for the spread of a mature epidemic, i.e. one characterized by an exponentially decaying growth rate of the cumulative number of cases/deaths - the speed of this decay being measured by the growth rate's half-life. If such a pattern is observed during the recent past, then it can be extrapolated. A spreadsheet is made available that allows users to input weekly cumulative numbers of deaths and obtain an estimate of the growth rate's baseline half-life and the corresponding projections. These projections can be compared to those with a larger half-life (if a protracted epidemic is expected, e.g. due to second wave), or with a smaller one (if successful therapies or mitigation efforts reduce transmission). The model is applied to deaths due to COVID-19 in California in May-June 2020.