Question

Rational Functions

In 1918, women were allowed to join the Marine Corps to handle the clerical duties, while the men fought in World War I. Prior to World War II, the United States Marine Corps Women’s Reserve was formed. Eventually Congress passed the Women’s Armed Services Integration Act. Women could then join the regular component of the Marine Corps, but the number of women could not exceed 2% of the total number of Marines.


By 1965, during the Vietnam War, there were 2700 women in the Marines. Women could participate in a wider variety of duties including radio operator, parachute rigger, quartermaster, auto mechanic, telegraph operator, and aerial gunnery instructor. But it was not until 1967 that a law was passed removing the restriction on the number of women in the Marines. In addition, women could be promoted to the rank of colonel. Within the next ten years, women would be able to work in all aspects of the Marine Corps except the infantry, artillery, armor, and the pilot/air crew.


In 2008, there were 9782 women in the Marine Corps on active duty, or about 5% of the Marines on active duty. Currently, women now receive combat training and are accepted into special skill schools that were traditionally only available to the male Marines. Also, women are working in non-traditional jobs and in certain other areas that were previously restricted. Women in the Marine Corps serve proudly and honorably next to their male counterparts in any area the United States Marine Corps requires. The number of women in the United States Marine Corps can be modeled by:


W = 414x^2 - 3341x + 9403 / 0.04x^2 - 0.32x + 1

where x is the number of years since 2000


Graph the model to find the number of women in the Marine Corps between 2000 and 2009.

Use your graph to estimate the number of female Marines in 2006.

Identify the x-intercepts of this function, if any.

Identify the vertical and horizontal asymptotes of the graph of this function, if any.

Use the function to estimate the number of women in the Marine Corps in 2015.

Give two reasons why the number of women in the Marine Corps could exceed your answer from Exercise 5.

Answer 1

• see attached for a graph
• 2006: 8,194
• no x-intercepts
• horizontal asymptote: y = 10,350; no vertical asymptotes
• 2015: 10,084
• no information on Exercise 5

Explanation:

a)

The graph is attached

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b)

The value for 2006 is shown in the table for x=6: 8,194.

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c)

The graph does not cross y=0. It has a minimum of about 7392.

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d)

The denominator is never zero, so there are no vertical asymptotes. The horizontal asymptote is the ratio of the x^2 coefficients, 414/0.04 = 10,350.

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e)

The value of the function for x=15 is 10,084. The number of women in the Marines in 2015 is modeled as 10,084.

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f)

No information is provided regarding Exercise 5 or its answer.