We present a systematic study of the steep decay emission from gamma-ray bursts (GRBs) observed by the Swift X-Ray Telescope (XRT). In contrast to the analysis described in recent literature, we produce composite Burst Alert Telescope (BAT) and XRT light curves by extrapolating the XRT data (2-10 keV) into the BAT energy range (15-25 keV) rather than extrapolating the BAT data into the XRT energy band (0.3 -10 keV). Based on the fits to the composite light curves, we have confirmed the existence of an exponential decay component which smoothly connects the BAT prompt data to the XRT steep decay for several GRBs. We also find that the XRT steep decay for some of the bursts can be well fit by a combination of a power law with an exponential decay model. We discuss this exponential component within the framework of both the internal and the external shock model.
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