We have studied the decay of a Bose-Einstein condensate of metastable helium atoms in an optical dipole trap. In the regime where two- and three-body losses can be neglected we show that the Bose-Einstein condensate and the thermal cloud show fundamentally different decay characteristics. The total number of atoms decays exponentially with time constant tau; however, the thermal cloud decays exponentially with time constant (4/3)tau and the condensate decays much faster, and non-exponentially. We show that this behaviour, which should be present for all BECs in thermal equilibrium with a considerable thermal fraction, is due to a transfer of atoms from the condensate to the thermal cloud during its decay.
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