How are polynomials used in your daily life?

Answer 1

Polynomials are used in various ways in daily life, such as in finance for calculating interest rates and investment returns, in engineering for modeling physical systems, and in computer graphics for creating curves and surfaces. They are also used in statistics for fitting data to a curve and in physics for describing the motion of objects. Overall, polynomials provide a versatile mathematical tool for analyzing and solving real-world problems across different fields.

Answer 2

Although many of us don't realize it, people in all sorts of professions use polynomials every day. The most obvious of these are mathematicians, but they can also be used in fields ranging from construction to meteorology. Although polynomials offer limited information, they can be used in more sophisticated analyses to retrieve more data.

What is a Polynomial?

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Polynomials are algebraic expressions that add constants and variables. Coefficients multiply the variables, which are raised to various powers by non-negative integer exponents.

How do People use Polynomials?

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.

Polynomials for Modeling or Physics

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Polynomials can also be used to model different situations, like in the Stock Market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.

Polynomials in Industry

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For people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen. For the rest of us, they are less apparent but we still probably use them to predict how changing one factor in our lives may affect another--without even realizing it.

Curve Fitting

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Polynomials are fit to data points in both regression and interpolation. In regression, a large number of data points is fit with a function, usually a line: y=mx+b. The equation may have more than one "x" (more than one dependent variable), which is called multiple linear regression.

In interpolation, short polynomials are joined together so they pass through all the data points. For those who are curious to research this more, the name of some of the polynomials used for interpolation are called "Lagrange polynomials," "cubic splines" and "Bezier splines."

Chemistry

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Polynomials come up often in chemistry. Gas equations relating diagnostic parameters can usually be written as polynomials, such as the ideal gas law: PV=nRT (where n is mole count and R is a proportionality constant).

Formulas of molecules in concentration at equilibrium also can be written as polynomials. For example, if A, B and C are the concentrations in solution of OH-, H3O+, and H2O respectively, then the equilibrium concentration equation can be written in terms of the corresponding equilibrium constant K: KC=AB.

Physics and Engineering

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Physics and engineering are fundamentally studies in proportionality. If a stress is increased, how much does the beam deflect? If a trajectory is fired at a certain angle, how far away will it land? Well-known examples from physics include F=ma (from Newton's laws of motion), E=mc^2 and F---r^2=Gm1---m2 (from Newton's law of gravitation, though usually the r^2 is written in the denominator).

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• Polynomials come up often in chemistry. Gas equations relating diagnostic parameters can usually be written as polynomials, such as the ideal gas law: PV=nRT (where n is mole count and R is a proportionality constant).

  Formulas of molecules in concentration at equilibrium also can be written as polynomials. For example, if A, B and C are the concentrations in solution of OH-, H3O+, and H2O respectively, then the equilibrium concentration equation can be written in terms of the corresponding equilibrium constant K: KC=AB.

Physics and Engineering

• Physics and engineering are fundamentally studies in proportionality. If a stress is increased, how much does the beam deflect? If a trajectory is fired at a certain angle, how far away will it land? Well-known examples from physics include F=ma (from Newton's laws of motion), E=mc^2 and F---r^2=Gm1---m2 (from Newton's law of gravitation, though usually the r^2 is written in the denominator).