The AraC family transcription factor MarA activates approximately 40 genes (the marA/soxS/rob regulon) of the Escherichia coli chromosome resulting in different levels of resistance to a wide array of antibiotics and to superoxides. Activation of marA/soxS/rob regulon promoters occurs in a well-defined order with respect to the level of MarA, however, the order of activation does not parallel the strength of MarA binding to promoter sequences. To understand this lack of correspondence, we developed a computational model of transcriptional activation in which a transcription factor either increases or decreases RNA polymerase binding, and either accelerates or retards post-binding events associated with transcription initiation. We used the model to analyze data characterizing MarA regulation of promoter activity. The model clearly explains the lack of correspondence between the order of activation and the MarA-DNA affinity and indicates that the order of activation can only be predicted using information about the strength of the full MarA-polymerase-DNA interaction. The analysis further suggests that MarA can activate without increasing polymerase binding and that activation can even involve a decrease in polymerase binding, which is opposite to the textbook model of activation by recruitment. These findings are consistent with published chromatin immunoprecipitation assays of interactions between polymerase and the E. coli chromosome. We find that activation involving decreased polymerase binding yields lower latency in gene regulation and therefore might confer a competitive advantage to cells. Our model yields insights into requirements for predicting the order of activation of a regulon and enables us to suggest that activation might involve a decrease in polymerase binding which we expect to be an important theme of gene regulation in E. coli and beyond.