Exponential Model Vs A Third Degree Polynomial Model Using Regressions.

This lesson allows you to perform an exponential regression and then with the same data a third degree polynomial regression and compare the resulting graphs and tables. The lesson uses crystal vases and as a volume measure a graduated beaker to pour a constant volume of colored water to the base and graphing the height vs the volume as this changes with each increment in volume. For each measure of water added to the vase, a coordinate point (volume, height) is generated. With several of these experimentally obtained points then a graphing calculator gets a regression model that can be lineal, quadratic, cubic, etc. The task is to determine which one is the best fit. You may interact with the lesson by marking the different heights as the volume measures are added to the vase and complete the provided table at the same time. Additionally, you might try to get the model yourself without the use of the graphing calculator. To mark the heights in the ruler you may use the MARKER TOOLS menu.

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Lesson's Glossary

 

Constant: It is a number or value that remains always the same. Never changes.

Exponent: It is a raised number representing the repeated multiplication of a given factor. Perfect square trinomial: A trinomial generated by the product of two equal binomials.

Expression: Any combination of numbers and operations without the = sign.

Factored Form: Any polynomial that is written as the product of polynomials of lower degree that may be obtained from the original polynomial.

Like terms: Terms that have the same combination of variables to the same power as factors.

Polynomial: A algebraic statement with one or more terms. Word comes from “poly” which means many.

Polynomial (third degree): Geometric representation. A third degree polynomial may be represented as the volume of a rectangular prism for which length, width and depth are the linear factors of the polynomial.

Power: Exponent of a number or variable.

Term: A form of grouping one or more numerical and/or variable factors by means of multiplication and division. Addition and subtraction symbols separate terms.

Variable: A letter used to represent a number. When the variable is part of an equation, it is possible to find the value for which it stands for by solving the equation. This is the solution (s) of the equation.

Variable expression: Mathematical phrase with at least one variable in it.

 

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