One of the major concerns in wireless sensor networks is improving the network lifetime. In this paper, we propose a new energy provisioning model and investigate the relationship between the network lifetime and the network density by using both simulations and analytic models. We show that the average amount of energy required to report an event to the sink decreases when sensor network density increases. Moreover, we demonstrate that the speed of increasing the network lifetime goes up faster than that of the network density. Based on this result, we prove that nodes must be deployed at the same time and not over different deployment phases.