Fig. 7 shows the S&P500 as a function of time since the plateau of the summer 2003, following a first rally after the minimum reached at the end of the first quarter of 2003. One can observe three approximately linear growth regimes with increasing slopes shown by the colored lines. Alternatively, this can be represented by an accelerating growth rate: in logarithmic scale such that an exponential growth with constant rate qualifies as a straight line, we still observe this upward curvature, characteristic of a super-exponential acceleration. Comparing with all our previous analyses previously published, such a behavior suggests the existence of a positive feedback and of herding behavior pushing the prices up. In general, such a regime should shift to another phase as it is unsustainable. In the present case, the new regime could take the form of a consolidation followed by a progressively growing correction as predicted in our previous figures. Or, as occurred following October 1997, a further accelerating growth could resume following a consolidating plateau. We are not able to make more precise statements with this approach, as the log-periodic patterns are not present in this putative bubble and the accelerating properties are not yet well-developed.