Sp99ex2 - Sp 99 EGN 3420 Exam 2 Name SHOW ALL WORK In each...

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Sp 99 EGN 3420 Exam 2 Name__________________ SHOW ALL WORK! In each problem, round all presented results to 4 places after the decimal point. Problem 1 (35 pts) A tutoring service has kept records of performance on a standardized test and the number of days students attend their review classes. The performance rating Y represents the per cent improvement in the test score students attain after taking the exam a second time. X is the number of attendance days in the review class. X, Attendance Days x 0 1 x 1 2.5 x 2 5 x 3 6.5 x 4 9 Y, % Improvement y 0 2 y 1 5 y 2 11 y 3 14 y 4 17 a) Estimate f (4), the % improvement in one's score after 4 days of attending review classes, assuming y = f ( x ) is the true function relating X and Y . Base your result on a third order Newton divided-difference interpolating polynomial f 3 ( x ). Fill in the table of divided differences below to find the appropriate coefficients. i x i y i 2 3 4 0 1 2 3 4 b) Estimate the error in the interpolated value f (4). Use the extra data point. i.e. the one not used in Part a) to obtain your answer.
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