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relationship between the death rate of men and the average number of hours per day that the men slept. These data are listed in the following table: 6 7 8 f(x) 1121 805 626 813 967 (Source: Morowitz, Harold J., "Hiding in the Hammond Report," Hospital Practice.) Here x is average number of hours of sleep, and f(x) the death rate per 100 000 males. a) Construct a backward difference table for the data. b) Use the backward difference table presented in a), along with Newton's backward difference formula, to approximate f(10) with a polynomial of degree 3, P3(x). Start with n =9.

relationship between the death rate of men and the average number of hours per day that the men slept. These data are listed in the following table: 6 7 8 f(x) 1121 805 626 813 967 (Source: Morowitz, Harold J., "Hiding in the Hammond Report," Hospital Practice.) Here x is average number of hours of sleep, and f(x) the death rate per 100 000 males. a) Construct a backward difference table for the data. b) Use the backward difference table presented in a), along with Newton's backward difference formula, to approximate f(10) with a polynomial of degree 3, P3(x). Start with n =9.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In a study by Dr. Harold J. Morowitz of Yale University, data were gathered that showed the relationship between the death rate of men and the average number of hours per day that the men slept. These data are listed in the following table: 7 8. 9 f (x) 1121 805 626 813 967 (Source: Morowitz, Harold J., "Hiding in the Hammond Report, Hospital Practice.) Here x is average number of hours of sleep, and f(x) the death rate per 100 000 males. a) Construct a backward difference table for the data. b) Use the backward difference table presented in a), along with Newton's backward difference formula, to approximate f(10) with a polynomial of degree 3, P3(x). Start with n=9.
Transcribed Image Text:In a study by Dr. Harold J. Morowitz of Yale University, data were gathered that showed the relationship between the death rate of men and the average number of hours per day that the men slept. These data are listed in the following table: 7 8. 9 f (x) 1121 805 626 813 967 (Source: Morowitz, Harold J., "Hiding in the Hammond Report, Hospital Practice.) Here x is average number of hours of sleep, and f(x) the death rate per 100 000 males. a) Construct a backward difference table for the data. b) Use the backward difference table presented in a), along with Newton's backward difference formula, to approximate f(10) with a polynomial of degree 3, P3(x). Start with n=9.
a) Construct a backward difference table for the data. b) Use the backward difference table presented in a), along with Newton's backward difference formula, to approximate f(10) with a polynomial of degree 3, P3(x). Start with Xn = = 9. c) Estimate the error in the approximation in b).
Transcribed Image Text:a) Construct a backward difference table for the data. b) Use the backward difference table presented in a), along with Newton's backward difference formula, to approximate f(10) with a polynomial of degree 3, P3(x). Start with Xn = = 9. c) Estimate the error in the approximation in b).
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