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We have carried out Very Large Array (VLA) continuum observations to studythe variability of Sgr A* at 43 GHz ($\lambda$=7mm) and 22 GHz($\lambda$=13mm). A low level of flare activity has been detected with aduration of $\sim$ 2 hours at these frequencies, showing the peak flareemission at 43 GHz leading the 22 GHz peak flare by $\sim20$ to 40 minutes. Theoverall characteristics of the flare emission are interpreted in terms of theplasmon model of Van der Laan (1966) by considering the ejection andadiabatically expansion of a uniform, spherical plasma blob due to flareactivity. The observed peak of the flare emission with a spectral index$\nu^{-\alpha}$ of $\alpha$=1.6 is consistent with the prediction that the peakemission shifts toward lower frequencies in an adiabatically-expandingself-absorbed source. We present the expected synchrotron light curves for anexpanding blob as well as the peak frequency emission as a function of theenergy spectral index constrained by the available flaring measurements innear-IR, sub-millimeter, millimeter and radio wavelengths. We note that theblob model is consistent with the available measurements, however, we can notrule out the jet of Sgr A*. If expanding material leaves the gravitationalpotential of Sgr A*, the total mass-loss rate of nonthermal and thermalparticles is estimated to be $\le 2\times10^{-8}$ M$_\odot$ yr$^{-1}$. Wediscuss the implication of the mass-loss rate since this value matches closelywith the estimated accretion rate based on polarization measurements.Comment: Revised with new Figures 1 and 2, 17 pages, 4 figures, ApJ (in press

Flaring Activity of Sagittarius A* at 43 and 22 GHz: Evidence for Expanding Hot Plasma