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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) 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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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: 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.
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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