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Chapter 2: Problem 81

Why is a third-degree polynomial function with a negative leading coefficient not appropriate for modeling nonnegative real-world phenomena over a long period of time?

Short Answer

Expert verified
A third-degree polynomial function with a negative leading coefficient is not appropriate for modeling nonnegative real-world phenomena over a long period because, eventually, it predicts negative outcomes, which isn't representative of real-world, nonnegative scenarios over time.

Step by step solution

01

Understanding polynomial functions and leading coefficients

A polynomial function's degree tells you its highest power of x. When a polynomial is third-degree, it means the highest power of x in the equation is 3. A leading coefficient refers to the coefficient of the term of highest degree in a given polynomial. If a third-degree polynomial has a negative leading coefficient, it affects the overall shape of the graph, causing it to start at positive infinity and end at negative infinity when moving from left to right.
02

Interpreting the graph

As x-values move toward positive or negative infinity, the y-values of a third-degree polynomial with a negative leading coefficient go to negative infinity. This means that the function will eventually become negative as time (or any other measurement along the x-axis) extends indefinitely.
03

Applying the understanding to real-world phenomena

For modeling nonnegative real-world phenomena over a long period of time, a function that allows for negative values is not appropriate. As time increases or rolls on, there won't be 'negative' time or measure in reality, so a function that predicts or implies negative values doesn't represent a realistic model.

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Most popular questions from this chapter

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