Chapter 5, Problem 16TP

Solution

(a)

To Find: Enrollment at two-year intervals for the years $1980\text{ to }2000$.

The enrollments are: $7.25,7.13,6.96,6.71,6.35,5.93,5.84,6.48,7.22,7.64,\text{ and }7.83$.

Given information:

The number $n$ (in millions) of males enrolled in high school in United States from $1980to2001$ can be modeled by: $n=\frac{0.0441x^2-1.08x+7.25}{0.00565x^2-0.142x+1.00}$ , where $x$ represents the number of years since $1980$.

Explanation:

Make table as below:

Year	$x$	$n$
$\begin{array}{l}1980\\ 1982\\ 1984\\ 1986\\ 1988\\ 1990\\ 1992\\ 1994\\ 1996\\ 1998\\ 2000\end{array}$	$\begin{array}{l}0\\ 2\\ 4\\ 6\\ 8\\ 10\\ 12\\ 14\\ 16\\ 18\\ 20\end{array}$	$\begin{array}{l}7.25\\ 7.13\\ 6.96\\ 6.71\\ 6.35\\ 5.93\\ 5.84\\ 6.48\\ 7.22\\ 7.64\\ 7.83\end{array}$

Therefore, the enrollments are $7.25,7.13,6.96,6.71,6.35,5.93,5.84,6.48,7.22,7.64,\text{ and }7.83$.

(b)

To graph: The given model.

Given information:

The number $n$ (in millions) of males enrolled in high school in United States from $1980to2001$ can be modeled by:

  $n=\frac{0.0441x^2-1.08x+7.25}{0.00565x^2-0.142x+1.00}$ , where $x$ represents the number of years since $1980$.

Graph:

The graph of the given model is:

  

Interpretation:

The graph falls initially but then it again rises.

(c)

To Find: The year in which $7.7$ million males were enrolled in high school using graph.

  $7.7$ million males were enrolled in high school in the year $1999$.

Given information:

The number $n$ (in millions) of males enrolled in high school in United States from $1980to2001$ can be modeled by:

  $n=\frac{0.0441x^2-1.08x+7.25}{0.00565x^2-0.142x+1.00}$ , where $x$ represents the number of years since $1980$.

Explanation:

Consider the graph of the given model.

  

Therefore, $7.7$ million males were enrolled in high school in the year $1999$.

(d)

To determine: The trend of the graph.

The graph has an increasing trend.

Given information:

The number $n$ (in millions) of males enrolled in high school in United States from $1980to2001$ can be modeled by:

  $n=\frac{0.0441x^2-1.08x+7.25}{0.00565x^2-0.142x+1.00}$ , where $x$ represents the number of years since $1980$.

Explanation:

Consider the graph of the given model.

  

The graph falls initially but then it again rises. Therefore, it has an increasing trend.