The population, f, of a small community on the outskirts of a city grew rapidly over a fifteen year period, as can be seen in the table: 10 15 f(x) 101 211 449 948 Here x denotes time (in years), while f(x) represents the size of the population of the community at time x. As an engineer working for an electricity company, you must find an approximation for what the population size was at time x=7.5, in order to estimate what the demand for electricity was at the time. a) Construct a forward difference table for the data. b) Use the forward difference table presented in a), along with Newton's backward difference formula, to approximate f(7.5) with a polynomial of degree 2, O2(x). Start with n = 15.
The population, f, of a small community on the outskirts of a city grew rapidly over a fifteen year period, as can be seen in the table: 10 15 f(x) 101 211 449 948 Here x denotes time (in years), while f(x) represents the size of the population of the community at time x. As an engineer working for an electricity company, you must find an approximation for what the population size was at time x=7.5, in order to estimate what the demand for electricity was at the time. a) Construct a forward difference table for the data. b) Use the forward difference table presented in a), along with Newton's backward difference formula, to approximate f(7.5) with a polynomial of degree 2, O2(x). Start with n = 15.
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 population, f, of a small community on the outskirts of a city grew rapidly over a fifteen year
period, as can be seen in the table:
5
10
15
f(x)
101
211
449
948
Here x denotes time
(in years), while f (x) represents the size of the population of the community at
time x.
As an engineer working for an electricity company, you must find an approximation for what the
population size was at time x=7.5, in order to estimate what the demand for electricity was at the time.
a) Construct a forward difference table for the data.
b) Use the forward difference table presented in a), along with Newton's backward difference formula, to
approximate f(7.5) with a polynomial of degree 2, 0, (x). Start with In = 15.
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