This paper uses computational experiments to explore the role of exposure in the emergence of construction grammars. While usage-based grammars are hypothesized to depend on a learner’s exposure to actual language use, the mechanisms of such exposure have only been studied in a few constructions in isolation. This paper experiments with (i) the growth rate of the constructicon, (ii) the convergence rate of grammars exposed to independent registers, and (iii) the rate at which constructions are forgotten when they have not been recently observed. These experiments show that the lexicon grows more quickly than the grammar and that the growth rate of the grammar is not dependent on the growth rate of the lexicon. At the same time, register-specific grammars converge onto more similar constructions as the amount of exposure increases. This means that the influence of specific registers becomes less important as exposure increases. Finally, the rate at which constructions are forgotten when they have not been recently observed mirrors the growth rate of the constructicon. This paper thus presents a computational model of usage-based grammar that includes both the emergence and the unentrenchment of constructions.