Adult-born neurons in the dentate gyrus (DG) functionally integrate into the behaviorally relevant hippocampal networks, showing a specific Arc-expression response to spatial exploration when mature. However, it is not clear when, during the 4- to 6-week interval that is critical for survival and maturation of these neurons, this specific response develops. Therefore, we characterized Arc expression after spatial exploration or cage control conditions in adult-born neurons from rats that were injected with BrdU on one day and were sacrificed 1, 7, 15, 30, and 45 days post-BrdU injection (PBI). Triple immunostaining for NeuN, Arc, and BrdU was analyzed through the different DG layers. Arc protein expression in BrdU-positive cells was observed from day 1 to day 15 PBI but was not related to behavioral stimulation. The specific Arc-expression response to spatial exploration was observed from day 30 and 45 in about 5% of the BrdU-positive cell population. Most of the BrdU-positive neurons expressing Arc in response to spatial exploration (∼90%) were located in DG layer 1, and no Arc expression was observed in cells located in the subgranular zone (SGZ). Using the current data and that obtained previously, we propose a mathematical model suggesting that new neurons are unlikely to respond to exploration by expressing Arc after they are 301 days old, and also that in a 7-month-old rat the majority (60%) of the neurons that respond to exploration must have been born during adulthood; thus, suggesting that adult neurogenesis in the DG is highly relevant for spatial information processing.