time (x₂) 12 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 to = 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: x, represents the end of a testing day, where the values of x, are as tabulated, while yi represents the number of positive tests conducted by the end of day x₁.)
time (x₂) 12 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 to = 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: x, represents the end of a testing day, where the values of x, are as tabulated, while yi represents the number of positive tests conducted by the end of day x₁.)
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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Transcribed Image Text:The table
time (x₂)
1
2 3 4 56
infections (y = f(xi)) 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 xo = 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: x, 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 x₁.)
(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(x). Start with xo = 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(x). Start with n = 6.
(ii) Estimate the error in the approximation in (c)(i).
(d) State whether P3(x) and Q3(x) give over or under approximations for f(7).
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