Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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..)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
See similar textbooks
icon
Related questions
Question
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).
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS