The prefrontal cortex is widely believed to play an important role in facilitating people's ability to switch performance between different tasks. We present a biologically-based computational model of prefrontal cortex (PFC) that explains its role in task switching in terms of the greater flexibility conferred by activation-based working memory representations in PFC, as compared with more slowly adapting weight-based memory mechanisms. Specifically we show that PFC representations can be rapidly updated when a task switches via a dynamic gating mechanism based on a temporal-differences reward-prediction learning mechanism. Unlike prior models of this type, the present model develops all of its internal representations via learning mechanisms as shaped by the demands of continuous periodic task switching. This advance opens up a new domain of research into the interactions between working memory task demands and the representations that develop to meet them. Results on a version of the Wisconsin Card Sorting task are presented for the full model and a number of comparison networks that test the importance of various model features.