Graphing active users over time

I am trying to construct a visualization of our system's active users over time. We arbitrarily define an active user as one that has made a logged within the last 7 days. Our source data for the visualization is a table containing the user and purchase dates like the table below.

What I would like to see is a line graph with the date on the x axis.

Manually calculating the values off the table above would give the following.

7/4

7/2

I have tried a number of things and can not seem to get the values that fit our definitions. The moving sum, on a cntd(User) counts distinct users in a single day, but does not count the distinct across days.

Thanks in advance for  your help.