Modify the Python function from the previous section so that it also returns the number of iterations required to arrive at the solution within the specified tolerance.

Use the customised Python function to create a table of the number of iterations needed 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 \(n\) given a tolerance of \(10^{-n}\).