Fast radio bursts (FRBs) are extremely powerful sources of radio waves observed at cosmological distances. We use a sophisticated model of FRB observations -- presented in detail in a companion paper -- to fit FRB population parameters using large samples of FRBs detected by ASKAP and Parkes, including seven sources with confirmed host galaxies. Our fitted parameters demonstrate that the FRB population evolves with redshift in a manner consistent with, or faster than, the star-formation rate (SFR), ruling out a non-evolving population at 99.9% C.L. Our estimated maximum FRB energy is $log_{10} E_{rm max} [{rm erg}] = 41.84_{-0.18}^{+0.49}$ (68% C.L.) assuming a 1,GHz emission bandwidth, with slope of the cumulative luminosity distribution $gamma=-1.16_{-0.12}^{+0.11}$. We find a log-mean host DM contribution of $145_{-60}^{+64}$,pc,cm$^{-3}$ on top of a typical local (ISM and halo) contribution of $sim80$,pc,cm$^{-3}$, which is higher than most literature values. These results are consistent with the model of FRBs arising as the high-energy limit of magnetar bursts, but allow for FRB progenitors that evolve faster than the SFR.
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