Q 2) (25 pts) Assume that we want to define a mathematical model that returns the location of ITUCAR within T campus according to time. The observed path of ITUCAR is represented with a tuple, (x, y) = (time, location). The observed locations of ITUCAR are (x0, y0) = (2, 1) and (x1, y1) = (7, 6).

b) (5 pts) Evaluate the interpolating function (the function you construct) for x=4.

c) (5 pts) Assume that we obtained additional points related to the path of ITUCAR, which points are (x2, y2)= (3, 3) and (x3, y3)= (5, 4). Find a Vendermode matrix with monomial basis = Xi. that considers all known points.

d) (5 pts) Assume that we want to know the location of ITUCAR at x=9. Do we have an interpolation for that point? Why? Explain