Dedicated I is a quest given by Henry in Nightfall Citadel. The quest log gives the following description:
The quest requires you to achieve 20 Dedication in the same week you accepted the quest.
Completing Dedicated IEdit
Once you have collected the required Dedication, talk to Henry in Nightfall Citadel and select the 'Dedicated I' option. Henry will thank you for your participation. You will be rewarded Experience Points.