Using the following table of points and using the polynomial method Newton-Gregory interpolants, Calculate the value of Y for X = 0.15 X = 0.45 (The difference table, the difference vector and the calculations necessary to obtain the requested results must be provided).

X Y

0 1.000000

0.1 0.799950

0.3 0.395953

0.4 0.187227

0.5 -0.031088