Use the Leading Coefficient Test to Determine the End Behavior

question 440

Multiple Choice

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-The following table shows the number of DWI arrests in a county for the years 1994-1998, where 1 represents 1994, 2 represents 1995, and so on. $$\begin{array} { c | c } \text { Year, x } & \text { DWI arrests, T } \\\hline 1994,1 & 4358.68 \\1995,2 & 4429.92 \\1996,3 & 4471.5 \\1997,4 & 4508 \\1998,5 & 4560\end{array}$$ This data can be approximated using the third-degree polynomial
$$T ( x ) = - 0.57 x ^ { 3 } + 0.59 x ^ { 2 } + 63.46 x + 4295.2$$
Use this function to predict the number of DWI arrests in 2007. Round to the nearest whole number.

• A) 3735
• B) 3745
• C) \(- 556\)
• D) 2847

---

Definitions:

Bar Graph

A chart that represents categorical data with rectangular bars with lengths proportional to the values they represent.

Frequency Polygon

Variation of a histogram where rather than a series of vertical bars, a line is drawn to connect the midpoint for each of the different measured variables in the distribution.

Central Tendency

A statistical measure that indicates the center or the middle of the distribution.

Extreme Outliers

Data points that are significantly distant from the majority of other points in a dataset, often indicating a deviation from expected norms.