Monday, October 24, 2016

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 72

The table below shows the median weekly salary of a union member for various years.

YearWeekly Salary(in dollars)20006962001718200274020037602004781

a. Determine the equation of the line between (2000, 696) and (2004, 781).

We let (x1,y1)=(2000,696) and (x2,y2)=(2004,781)

Using the slope of the line,


m=y2y1x2x1m=78169620042000m=854


Using the Point Slope Formula, where m=854 and (x1,y1)=(2000,696)


yy1=m(xx1)y696=854(x2000)Substitute m=854 and (x1,y1)=(2000,696)y696=854x500Apply Distributive Propertyy=854x500+696Simplifyy=854x+196


b. What was the average annual rate of change in the median weekly salary for a union employee between 2000 and 2004?


average rate of change=weekly salary from 2004 - weekly salary from 200020042000=78169620042000=854=21.25


The average annual rate of change in the median weekly salary for a union employee between 2000 and 2004 is $21.25.

c. Suppose the trend shown by the equation in part a were to continue, what would be the median weekly salary of a union worker in 2012?

Since the rate of change is linear, the slope is the same for any points. So we let (x1,y1)=(2000,696) and (x2,y2)=(2012,n), m=854, then


854=n69620122000854=n69612Multiply both sides by 12255=n696Add 696n=951


The median weekly salary of a union worker in 2012 is $951.

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