import math


def productivity(affinity_count):
    """ Return number representing productivity given the affinity count
    e.g. if you have nothing, we still automatically produce, but if there
    is someone, it will produce more efficiently.
    """
    if affinity_count == 0:
        return 0.3
    return 0.419874 * math.log(11.2406 * affinity_count)