  The dynamics of evaporative cooling of magnetically trapped $^{87}$Rb atoms
is studied on the basis of the quantum kinetic theory of a Bose gas. We carried
out the quantitative calculations of the time evolution of conventional
evaporative cooling where the frequency of the radio-frequency magnetic field
is swept exponentially. This "exponential-sweep cooling" is known to become
inefficient at the final stage of the cooling process due to a serious
three-body recombination loss. We precisely examine how the growth of a
Bose-Einstein condensate depends on the experimental parameters of evaporative
cooling, such as the initial number of trapped atoms, the initial temperature,
and the bias field of a magnetic trap. It is shown that three-body
recombination drastically depletes the trapped $^{87}$Rb atoms as the system
approaches the quantum degenerate region and the number of condensed atoms
finally becomes insensitive to these experimental parameters. This result
indicates that the final number of condensed atoms is well stabilized by a
large nonlinear three-body loss against the fluctuations of experimental
conditions in evaporative cooling.
