See https://metatalk.metafilter.com/26137/MetaFilter-Usage-Statistics#1406552 for details

mefi_active_user_sim.py

#!/usr/bin/env python3

activity_curve = [
        # This first part of the activity curve comes from the average values
        # from 2005-2021 This is the average of the non 2000-2004 values in [1].
        # See the MetaTalk thread [2] for more details.
        #
        # [1]: https://hack.wesleyac.com/mefi_percent_users_active_by_join_year_normalized.png
        # [2]: https://metatalk.metafilter.com/26137/MetaFilter-Usage-Statistics#1406552
        1.0000, 0.7942, 0.7185, 0.6773, 0.6419, 0.6161, 0.5868, 0.5625, 0.5440, 0.5194, 0.5039, 0.4876, 0.4758, 0.4671, 0.4539, 0.4404, 0.4210, 0.3977,
        # The scound part is a linear extrapolation, losing 1.735% of users per
        # year, which is the average of the last four differences in the
        # previous line. A linear extrapolation isn't great, but it does not
        # make a large difference to the fundamental point behind this
        # analysis.
        0.3803, 0.3630, 0.3456, 0.3283, 0.3109, 0.2936, 0.2762, 0.2589, 0.2415, 0.2242, 0.2068, 0.1895, 0.1721, 0.1548, 0.1374, 0.1201, 0.1027, 0.0854, 0.0680, 0.0507, 0.0333, 0.0160
]

def steady_state_users(joins, first_year_rate, activity_curve):
    t = 0
    for remaining_percent in activity_curve:
        remaining_percent = remaining_percent - (1 - first_year_rate)
        if remaining_percent > 0:
            t += joins * remaining_percent
    return t

# This is a simulation with the numbers from 2021
print(steady_state_users(587, 0.55, activity_curve))  # == 1349.513

# And with some hypothetical improvements in first-year activity rate or new user signups
print(steady_state_users(587, 0.65, activity_curve))  # == 2378.1718
print(steady_state_users(1340, 0.51, activity_curve)) # == 2377.964