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Instruction: Apply one decimal place rounding to calculations where applicable. The table time (r.) 1 2 3 4 5 6 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly infected individuals with a contagious, airborne disease at intervals of 1 day over a period of 6 days. Here i=0,1,2,...,5 and the quantities zo = 1 and % 32, respectively, represent the end of the first day of testing for the disease, and number of positive tests conducted by the end of that day. (Note: z, represents the end of a testing day, where the values of r, are as tabulated, while y, represents the number of positive tests conducted by the end of day z..)

Instruction: Apply one decimal place rounding to calculations where applicable. The table time (r.) 1 2 3 4 5 6 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly infected individuals with a contagious, airborne disease at intervals of 1 day over a period of 6 days. Here i=0,1,2,...,5 and the quantities zo = 1 and % 32, respectively, represent the end of the first day of testing for the disease, and number of positive tests conducted by the end of that day. (Note: z, represents the end of a testing day, where the values of r, are as tabulated, while y, represents the number of positive tests conducted by the end of day z..)

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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Instruction: Apply one decimal place rounding to calculations where applicable. The table time (r.) 1 2 3 456 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly infected individuals with a contagious, airborne disease at intervals of 1 day over a period of 6 days. Here i = 0, 1, 2,..., 5 and the quantities zo = 1 and yo = 32, respectively, represent the end of the first day of testing for the disease, and number of positive tests conducted by the end of that day. (Note: r, represents the end of a testing day, where the values of x, are as tabulated, while y, represents the number of positive tests conducted by the end of day z..) (a) Construct a forward difference table for the above data. (b) (i) Use the table presented in (a), along with Newton's forward difference formula, to approximate f(7) with a polynomial of degree 3, P3(r). Start with zo = 1. (ii) Estimate the error in the approximation in (b)(i). (c) (i) Use the table presented in (a), along with Newton's backward difference formula, to approximate f(7) with a polynomial of degree 3, Q3(2). Start with ₂ = 6. (ii) Estimate the error in the approximation in (c)(i). (d) State whether P3(r) and Q3(r) give over or under approximations for f(7).
Transcribed Image Text:Instruction: Apply one decimal place rounding to calculations where applicable. The table time (r.) 1 2 3 456 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly infected individuals with a contagious, airborne disease at intervals of 1 day over a period of 6 days. Here i = 0, 1, 2,..., 5 and the quantities zo = 1 and yo = 32, respectively, represent the end of the first day of testing for the disease, and number of positive tests conducted by the end of that day. (Note: r, represents the end of a testing day, where the values of x, are as tabulated, while y, represents the number of positive tests conducted by the end of day z..) (a) Construct a forward difference table for the above data. (b) (i) Use the table presented in (a), along with Newton's forward difference formula, to approximate f(7) with a polynomial of degree 3, P3(r). Start with zo = 1. (ii) Estimate the error in the approximation in (b)(i). (c) (i) Use the table presented in (a), along with Newton's backward difference formula, to approximate f(7) with a polynomial of degree 3, Q3(2). Start with ₂ = 6. (ii) Estimate the error in the approximation in (c)(i). (d) State whether P3(r) and Q3(r) give over or under approximations for f(7).
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