Delay in the nervous system is a serious issue for an organism that needs to act in real time. For example, during the time a signal travels from a peripheral sensor to the central nervous system, a moving object in the environment can cover a significant distance which can lead to critical errors in the effect of the corresponding motor output. This paper proposes that facilitating synapses which show a dynamic sensitivity to the changing input may play an important role in compensating for neural delays, through extrapolation. The idea was tested in a modified 2D pole-balancing problem which included sensory delays. Within this domain, we tested the behavior of recurrent neural networks with facilitatory neural dynamics trained via neuroevolution. Analysis of the performance and the evolved network parameters showed that, under various forms of delay, networks utilizing extrapolatory dynamics are at a significant competitive advantage compared to networks without such dynamics. In sum, facilitatory (or extrapolatory) dynamics can be used to compensate for delay at a single-neuron level, thus allowing a developing nervous system to stay in touch with the present environmental state.