Consider the improved Euler's method that averages two slopes, the slope obtained at the beginning of the step and the slope obtained at the end of the step, to improve our accuracy. Assume y_n+1=y_n+(h/2) ∗[g(t_n, y_n)+g(t_n+1, y_n+1)]. Let y′=0.25ty, y (0) = 2, and use the improved Euler's method with step sizes of 1, 0.5, and 0.1.