Software libraries are widely used by both industrial and open source client projects. Ideally, a client user of a library should adopt the latest version that the library project releases. However, sometimes the latest version is not better than a previous version. This is because the latest version may include additional developer effort to test and integrate all changed features. In this study, our main goal is to better understand the relationship between adoption of library versions and its release cycle. Specifically, we conducted an empirical study of release cycles for 23 libraries and how they were adopted by 415 Apache Software Foundation (ASF) client projects. Our findings show that software projects are quicker to update earlier rapid-release libraries compared to library projects with a longer release cycle. Moreover, results suggest that software projects are more likely to adopt the latest version of a rapid-release library compared to libraries with a longer release cycles.