def METHOD_NAME(rate, td, tb, max_k=100, save_to=None):
    """Test that A is well-behaved.
    Check that Ak ->r0**2tb**2 for k->infty, as per Eq. 43 in
    Zhang+95.
    """
    tau = 1 / rate
    r0 = r_det(td, rate)
    value = r0**2 * tb**2
    fig = plt.figure()
    for k in range(max_k):
        plt.scatter(k, A(k, r0, td, tb, tau), color="k")
    plt.axhline(value, ls="--", color="k")
    plt.xlabel("$k$")
    plt.ylabel("$A_k$")
    if save_to is not None:
        plt.savefig(save_to)
        plt.close(fig)