Implement the regula falsi method in Python, that is, define the following Python function:

def regula_falsi_solve(f, a, b, tol=0.001, maxiter=100):
    """
    Find the zero of a function f between a and b using the
    Regula Falsi Method with tolerance tol (default: 0.001) and 
    maximum number of iterations equal to maxiter (default: 1000)
    """

In addition to the approximation of the zero, make sure that the function also returns the number of iterations needed. Apply the regula_falsi_solve function to the polynomial $x^3+2x-1$ on the interval $[0,1]$ once with the default value of the tolerance to see if everything works correctly.

Then apply the Python function to create a table of the number of iterations required for tolerance $10^{-1}, 10^{-2}, 10^{-3},\ldots, 10^{-15}$. Verify that there is indeed a linear relationship between the number of iterations required $i_n$ and the natural number $n$ at a tolerance of $10^{-n}$.