We have carried out Very Large Array (VLA) continuum observations to study the variability of Sgr A* at 43 GHz ( lambda =7mm) and 22 GHz ( lambda =13mm). A low level of flare activity has been detected with a duration of 2 hours at these frequencies, showing the peak flare emission at 43 GHz leading the 22 GHz peak flare by 20 to 40 minutes. The overall characteristics of the flare emission are interpreted in terms of the plasmon model of Van der Laan (1966) by considering the ejection and adiabatically expansion of a uniform, spherical plasma blob due to flare activity. The observed peak of the flare emission with a spectral index nu - alpha of alpha =1.6 is consistent with the prediction that the peak emission shifts toward lower frequencies in an adiabatically-expanding self-absorbed source. We present the expected synchrotron light curves for an expanding blob as well as the peak frequency emission as a function of the energy spectral index constrained by the available flaring measurements in near-IR, sub-millimeter, millimeter and radio wavelengths. We note that the blob model is consistent with the available measurements, however, we can not rule out the jet model of Sgr A*. If expanding material leaves the gravitational potential of Sgr A*, the total mass-loss rate of nonthermal and thermal particles is estimated to be <= 2*10-8 Mo yr-1. We discuss the implication of the mass-loss rate since this value matches closely with the estimated accretion rate based on polarization measurements.