Given X: 0 10 16 Y: 6 16 28 The interpolated value X=4 using piecewise linear…

To find the interpolated value at X=4, identify the interval containing this point. The given data points are (0, 6), (10, 16), and (16, 28). Since X=4 lies between 0 and 10, we use the first interval.

Apply the piecewise linear interpolation formula: y = y_0 + (x - x_0) / (x_1 - x_0) * (y_1 - y_0). Substituting the values from the first interval: y = 6 + (4 - 0) / (10 - 0) * (16 - 6).

Calculate the result: y = 6 + (4 / 10) * 10 = 6 + 4 = 10. The interpolated value for X=4 is 10.