The tabletime (x₂)12 3 4 56infections (y = f(xi)) 32 37 34 48 53 69depicts the number of newly infected individuals with a contagious, airborne disease atintervals of 1 day over a period of 6 days. Here i = 0, 1, 2, ..., 5 and the quantities xo = 1and yo = 32, respectively, represent the end of the first day of testing for the disease, andnumber 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, whiley 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, toapproximate 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, toapproximate 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).

Answered: Image /qna-images/answer/5030ddaa-3201-4390-b44b-3b27a62b6186.jpg

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.)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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