Children at about age 18 months experience acceleration in word learning. This vocabulary explosion is a robust phenomenon, although the exact shape and timing vary from child to child. One class of explanations, which we term collectively as leveraged learning, posits that knowledge of some words helps with the learning of others. In this framework, the child initially knows no words and so learning is slow. As more words are acquired, new words become easier and thus it is the acquisition of early words that fuels the explosion in learning. In this paper we examine the role of leveraged learning in the vocabulary spurt by proposing a simple model of leveraged learning. Our results show that leverage can change both the shape and timing of the acceleration, but that it cannot create acceleration if it did not exist in the corresponding model without leveraging. This model is then applied to the Zipfian distribution of word frequencies, which confirm that leveraging does not create acceleration, but that the relationship between frequency and the difficulty of learning a word may be complex.