By digitally imaging colonies with more than a hundred cells, the distributions of cell size and shape are determined for four examples of 2-Ga microfossils: bacillus-shaped Eosynechococcus moorei and three dyads or diplococci (Sphaerophycus parvum and two forms of Eoentophysalis belcherensis). By assuming that each colony obeys steady-state growth, the measured distributions can be inverted to infer the time evolution of the individual cell shape. The time evolution can also be predicted analytically from rate-based models of cell growth, permitting the data to distinguish among different postulates for the physical principles governing growth. The cell cycles are found to be best described by the exponential growth of cell volume, although linear volume growth is not ruled out. However, the measured dyad cycles are inconsistent with several growth models based on surface area or the behavior of the septum at the division plane. Where they have been measured, modern bacilli obey exponential growth whereas eukaryotics obey linear growth, which implies that these 2-Ga microfossils are likely prokaryotic.