How to make this Retention calc into a Forumla?

I need to estimate the total number of times users logged in to an app, cumulatively at the end of a year. If I have a mobile app, and 100,000 people download it. And they only use it once, then the total active usage would be 100,000 - at end of year (365 days).
Lets say I have 70% retention. This means that everyday, people join, and 70% come back the next day. How can i work out the number of times the app was used at the end of a whole year?
100,000 people divided by 365 is around 274 (if everyday 274 people register, in One year it will be 100,000 people).
A = 274.
1st day B = A + (A - (A x .7 ))
2nd day C = B + (B - (B x .7))
How to work out for 365th? for whole year?
I need to make this into a formula to put in a forecast spreadsheet (using Numbers on Mac).
Thanks for your help.

In Column C how would I get the Downloaded to increase by a given %.
Assuming you want a daily download growth rate, you could do something like this:
In cell C2:  =Assumptions::$A
In cell C3, copied down:  =C2×(1+Assumptions::$B)
Rows 10 through 364 are hidden for screenshot.
SG

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