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2 Consider the function y = f(x) used to give the data in the chart below. a) [4] What degree, n of a polynomial models this data (use finite differences, and technology)? X 6 108 DULAWN- 1470 6650 19656 45936 92378 8 167310 b) Investigate the process of finding a function that exactly goes through all of these data points. i) [1]Create an equation of the iv) [1]Substitute the next point (1, -4) to form f(x) = ax" + bx"-+ cx"-?+ ... by create an equation of b, c and d. substituting the n value you discovered in Simplify, label this as equation 1. part a). ii) [1]Substitute the first point (0, 6) into V ) [1]Substitute the next point (2, 108) to the equation to show that the constant create an equation of b, c and d. term is 6. Simplify, label this as equation 2. vi) [1]Substitute the point (3, 1470) to iii) [1]Calculate a (using your answer from create an equation of b, c and d. le) and substitute a and e. Simplify, label this as equation 3. (b f(x) = ax"+ bx"-1+ cx"-2+... te vii) [1 ]eliminate "d" from equations 1 and 2 to create equation 4. viii) [1 ]eliminate "d" from equations 1 and 3 to create equation 5. ix) [2]Solve the resulting system of two equations to discover "b" and "c" [1]What is the and of a total function y = f(x)