High Dynamic Range (HDR) displays are capable of displaying a wider dynamic range of values than conventional displays. As HDR content becomes more ubiquitous, the use of these displays is likely to accelerate. As HDR displays can present a wider range of values, traditional strategies for mapping HDR content to Low Dynamic Range (LDR) displays can be replaced with either directly displaying values, or using a simple shift mapping (exposure adjustment). The latter approach is especially important when considering ambient lighting, as content viewed in a dark environment may appear substantially different to a bright one. This work seeks to identify an exposure value which is suitable for displaying specific HDR content on an HDR display under a range of ambient lighting levels. Based on data captured with human participants, this work establishes user preferred exposure values for a variety of maximum display brightnesses, content and ambient lighting levels. These are then used to develop two models to predict the preferred exposure. The first is based on linear regression using straightforward image statistics which require minimal computation and memory to be computed, making this method suitable to be directly used in display hardware. The second is a model based on Convolutional Neural Networks (CNN) to learn image features which best predict exposure values. The CNN model generates better results than the first model at the cost of memory and computation time.