Chapter 7.1, Problem 51PPS

(a).

To determine

Write a function that models the total number of men and women employed in the United States during this time.

Answer to Problem 51PPS

  $y=2085.6x+123,060$

Explanation of Solution

Given:

The number of women and men age 16 and over employed each year in the United States can be modeled by the following equations, where x is the number of years since 1994 and y is the number of people in thousands.

women : $y=1086.4x+56,610$

men: $y=999.2x+66,450$

Calculation:

For the total number of men and women employed in the United States during this time , that is , since 1994 ,

We have to add the number of women and men (in thousands) , so the function will be:

  $\begin{array}{l}y=1086.4x+56,610+999.2x+66,450\\ \Rightarrow y=2085.6x+123,060\end{array}$

where x is the number of years since 1994 and y is the number of people in thousands.

(b).

To determine

If f is the function for the number of men, and g is the function for the number of women , what does $\left(f-g\right)(x)$ represent

Answer to Problem 51PPS

  $\left(f-g\right)(x)$ is the difference in the employment of men and women.

Explanation of Solution

Given:

The number of women and men age 16 and over employed each year in the United States can be modeled by the following equations, where x is the number of years since 1994 and y is the number of people in thousands.

women : $y=1086.4x+56,610$

men: $y=999.2x+66,450$

Calculation:

  $\left(f-g\right)(x)$ represents the difference between the number of women and men employed each year in the United States since 1994.

Or, in other words , it is the difference in the employment of men and women.