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 \(10^{-n}\).