Humans are efficient continual learning systems; we continually learn new skills from birth with finite cells and resources. Our learning is highly optimized both in terms of capacity and time while not suffering from catastrophic forgetting. In this work we study the efficiency of continual learning systems, taking inspiration from human learning. In particular, inspired by the mechanisms of sleep, we evaluate popular pruning-based continual learning algorithms, using PackNet as a case study. First, we identify that weight freezing, which is used in continual learning without biological justification, can result in over $2\times$ as many weights being used for a given level of performance. Secondly, we note the similarity in human day and night time behaviors to the training and pruning phases respectively of PackNet. We study a setting where the pruning phase is given a time budget, and identify connections between iterative pruning and multiple sleep cycles in humans. We show there exists an optimal choice of iteration v.s. epochs given different tasks.