l . (Problem 6.4) (a) (20 points) Using Experimental data in the Table 1, apply the Gregory- Newton forward interpolation formula to evaluate function at x = 1. (b) (20 points) Using Experimental data in the Table 1, apply the Gregory- Newton backward interpolation formula to evaluate function at x = 78. (c) (10 points) write a code that uses Gregory-Newton forward interpolation formulas and evaluate function at x = 5- (d)(10 points) write a code that uses Gregory-Newton backward interpolation formulas and evaluate function at x = 65. Hint: You need to choose the are close to the point that you want to evaluate the function at that point. You need to assign i values accordingly. Note: I could name the independent variable r instead of x and it would not change the results Table 1: Data of .enicillin fermentation Penicillin Concentration unitsme