to estimate what the demand for electricity was at the time. a) Construct a backward difference table for the data. b) Use the backward difference t able

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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)
100
212
448
949
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
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: 10 15 f(x) 100 212 448 949 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
to estimate what the
demand for electricity
was
at the time.
a) Construct a backward
difference table for the
data.
b) Use the backward
difference table
presented in a), along
with Newton's backward
difference formula, to
approximate f(7.5) with a
polynomial of degree 2,
P2(x). Start with
Xn
15.
c) Estimate the error in
the approximation in b).
Transcribed Image Text:to estimate what the demand for electricity was at the time. a) Construct a backward difference table for the data. b) Use the backward difference table presented in a), along with Newton's backward difference formula, to approximate f(7.5) with a polynomial of degree 2, P2(x). Start with Xn 15. c) Estimate the error in the approximation in b).
Expert Solution
Step 1

The function value at a point can be interpolated using newton's backward difference interpolation formula. The formula is given as y(x)=yn+pyn+p(p+1)2!2yn+p(p+1)(p+2)3!3yn.

Here, p can be obtained using the formula p=x-xnh. The variable h is the step size.

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