Answer Set Programming Modulo Theories is a new framework of tight integration of answer set programming (ASP) and satisfiability modulo theories (SMT). Similar to the relationship between first-order logic and SMT, it is based on a recent proposal of the functional stable model semantics by fixing interpretations of background theories. Analogously to a known relationship between ASP and SAT, "tight" ASPMT programs can be translated into SMT instances. We demonstrate the usefulness of ASPMT by enhancing action language C+ to handle continuous changes as well as discrete changes. We reformulate the semantics of C+ in terms of ASPMT, and show that SMT solvers can be used to compute the language. We also show how the language can represent cumulative effects on continuous resources.