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Lower heating of our planet by the young Sun was compensated by higher warming from factors such as greater greenhouse gas concentrations or reduced albedo. Earth's climate history has therefore been one of increasing solar forcing through time roughly cancelled by decreasing forcing due to geological and biological processes. The current generation of coupled carbon-cycle/climate models suggests that decreasing geological forcing-due to falling rates of outgassing, continent growth, and plate spreading-can account for much of Earth's climate history. If Earth-like planets orbiting in the habitable zone of red dwarfs experience a similar history of decreasing geological forcing, their climates will cool at a faster rate than is compensated for by the relatively slow evolution of their smaller stars. As a result, they will become globally glaciated within a few billion years. The results of this paper therefore suggest that coupled carbon-cycle/climate models account, parsimoniously, for both the faint young Sun paradox and the puzzle of why Earth orbits a relatively rare and short-lived star-type.