Cerebral blood flow (CBF) plays a central role in the blood oxygen level dependent (BOLD) signal measured by functional magnetic resonance imaging (fMRI). Yet, age-related changes in CBF and its relationship with the BOLD response have not been studied extensively in typically developing children. Historically, positron emission tomography (PET) and single photon emission computed tomography (SPECT) have been used to study CBF during development. PET and SPECT studies have found that CBF increases rapidly in the first years of life, is elevated in childhood, and declines to adult levels in adolescence. However, due to their invasiveness, PET and SPECT studies have been limited to clinical contexts and measurements of CBF either at rest or with sedation. In addition to developmental change in CBF, studies of exercise and brain function with children (cognitive, electrophysiological, and fMRI experiments) suggest that level of physical activity affects CBF. The primary aims of this thesis were to assess whether there are age-related changes in CBF and BOLD hemodynamics during a functional task and whether there is a relationship between participants' level of physical activity and CBF measurements. To do so, this project used a noninvasive MRI method, arterial spin labeling (ASL), to examine CBF during rest and functional activity in typically developing children. Further, this study used an ASL technique, Quantitative Imaging of Perfusion using a Single Subtraction (QUIPSS), which simultaneously collects CBF and BOLD-weighted images to directly examine the relationship between CBF and the BOLD response. Participants included 8-year-old children (n = 8), 12-year-old children (n = 10), and adults 22-28 years of age (n = 9). This experiment focused on CBF in the motor cortex where stimulation with a finger tapping task was predicted to elicit a robust CBF and BOLD response. CBF was measured during a resting state scan. From functional images acquired during the task, three measurements were derived: absolute CBF change, percent CBF change, and percent BOLD change. These measures were calculated as the absolute or percent change in signal between rest and peak activity. In addition, both participant and parent reports of participants' physical activities six months prior to the scan were retrospectively obtained with a survey. Age group comparisons of the hemodynamic measures showed that 8-year-old children and 12-year-old children had significantly greater resting CBF levels than adults. There were no significant differences in resting CBF levels between 8-year-old children and 12-year-old children. Eight year olds had significantly greater absolute CBF change than adults. No significant age-related differences were observed for percent CBF and BOLD signal change. Analyses of the relationship between physical activity level and CBF showed that neither participant-reported nor parent-reported amounts of activity were related to the hemodynamic measures. This result may be due to higher than expected activity levels across the sample. Lastly, the finding that CBF is higher in children compared to adults without a corresponding elevation in BOLD signal suggests that additional physiological mechanisms that are elevated in childhood may offset the high CBF and result in a stable BOLD effect.