The prevalence of location tracking systems has resulted in large volumes of spatiotemporal data generated every day. Addressing reachability queries on such datasets is important for a wide range of applications (surveillance, public health, social networks, etc.) A spatiotemporal reachability query identifies whether a physical item (or information etc.) could have been transferred from the source object $O_S$ to the target object $O_T$ during a time interval $I$ (either directly, or through a chain of intermediate transfers). In previous research on spatiotemporal reachability queries, the number of such transfers is not limited, and the weight of a piece of transferred information remains the same. This paper introduces novel reachability queries, which assume a scenario of information decay. Such queries arise when the value of information that travels through the chain of intermediate objects decreases with each transfer. To address such queries efficiently over large spatiotemporal datasets, we introduce the RICCdecay algorithm. Further, the decay scenario leads to an important extension: if there are many different sources of information, the aggregate value of information an object can obtain varies. As a result, we introduce a top-k reachability problem, identifying the k objects with the highest accumulated information. We also present the RICCtopK algorithm that can efficiently compute top-k reachability with transfer decay queries. An experimental evaluation shows the efficiency of the proposed algorithms over previous approaches.