Evolving starburst galaxies, faint number counts, and the 2 keV background

Blue and 60 micron extragalactic number counts and redshift distributions are modeled using evolutionary models in which galaxies periodically undergo transient starburst events. Support is found for the hypothesis that the same starburst phenomenon is responsible for the excess source counts seen at both wavelengths, though observed at lower mean redshift in the far infrared than in the blue. The soft X-ray emission from these evolving starburst events is not likely to exceed the 2 keV background unless the evolutionary rate is greater than (1 + z)-cubed (luminosity or density evolution) and the redshift of galaxy formation is greater than about five.