Search requires individuals to balance exploration (finding new resources) with exploitation (making use of current resources) over time. How individuals perceive reward in a temporally extended search may significantly influence their explore/exploit decisions. Furthermore, how individuals perceive reward is related to impulsivity. Different aspects of impulsivity can lead to different predictions for people's search patterns. We tested some of these predictions in a search task with a non-depleting condition where resources would maintain value when exploited, and a depleting condition where resources lost value when exploited. Participants with larger temporal discounting rates (greater impulsivity) started exploiting depleting resources later than those with smaller discount rates, surprisingly appearing more patient and performing closer to the optimal level. However, this difference disappeared when resources were non-depleting. Greater impulsivity might make individuals more risk-seeking in the depleting search environment and thus explore depleting resources longer at the beginning phase of the search task.