  We examine a model in which a nonequilibrium phase transition from an active
to an extinct state is observed. The order of this phase transition has been
shown to be either continuous or first-order, depending on the parameter values
and the dimension of the system. Using increasingly large clusters, we use the
cluster approximation method to obtain estimates for the critical points in 1+1
dimensions. For the continuous phase transitions only, extrapolations of these
approximations show excellent agreement with simulation results. Further, the
approximations suggest that, consistent with simulation results, in 1+1
dimensions no first-order phase transitions are observed.
