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Modeling data with polynomial functions and rational functions

(1) Create a set of data that can be modeled as a polynomial function. Please provide a reference to the data. Plot the data using Microsoft Excel including the equation for the fit. Discuss how closely the data seem to match to the best fit line.

(2) Do the same for data that can be modeled using a rational function. Include in your answer how this can be used in a real-life application.

Solution Preview

Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileage at two different speeds, V1 and V2, the gas required varies as (V1/V2), raised to the third power, (V1/V2)3.

Rational functions are also useful. For example, a cubic/cubic model can be used to explain the thermal expansion of metals with temperature. Rational functions have been used to describe problems as diverse as the movement of blood through the body to how to produce items at the lowest possible cost.

For this Discussion Board, create a set of data that can be modeled as a polynomial function. Please provide a reference to the data. Plot the data using Microsoft Excel including the equation for the fit. Discuss how closely the data seem to match to the best fit line. Do the same for data that can be modeled using a rational function. Include in your answer how this can be used in a real-life application.

First things first ... a function is an equation relating two variables (usually called x and y) so that when you pick a value for x, there's only one possible value for y to make the equation true.

A polynomial function is a function where all the terms with x in them have coefficients that are real numbers and exponents that are whole numbers. (Some more definitions: a coefficient is the number that the variable is multiplied by, and an exponent is the power that the variable is raised to. Whole numbers are 0, 1, 2, 3, ...) Some examples of polynomials are:
y = x
y = -3x + 5
y = 3
y = 3x2 - 8x + 1
y = 8x95 + ...

Solution Summary

The solution includes definitions of the terms "function", "polynomial function", and "rational function". It explains through examples how to use Excel to model data using polynomial and rational functions.

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