In an increasingly automated world, trust between humans and autonomous systems is critical for successful integration of these systems into our daily lives. In particular, for autonomous systems to work cooperatively with humans, they must be able to sense and respond to the trust of the human. This inherently requires a control-oriented model of dynamic human trust behavior. In this paper, we describe a gray-box modeling approach for a linear third-order model that captures the dynamic variations of human trust in an obstacle detection sensor. The model is parameterized based on data collected from 581 human subjects, and the goodness of fit is approximately 80% for a general population. We also discuss the effect of demographics, such as national culture and gender, on trust behavior by re-parameterizing our model for subpopulations of data. These demographic-based models can be used to help autonomous systems further predict variations in human trust dynamics.