What model to fit pseudo-logarithmic trend?
One option is to take a curve fitting approach. For example, scipy.optimize.curve_fit.
Something like this:
import numpy as np
from scipy.optimize import curve_fit

def f(x, a, b, c):
    &quot;Rough functional form of the data&quot;
    return a + b * (1 - np.exp(-c/x))

solution = curve_fit(f, c, y, p0=(3_500, 3_500, 200))