There were 7,404,000 unemployed American workers in 1995. In 1980, there were 7,637,000 Americans unemployed.
a. What was the average change in unemployment for each of these 15 years?
b. If this decline continues at the same rate, how many Americans will be unemployed in the year 2055?
There are several ways to solve this. you can think of this as a linear equation with the points
(1980, 7,637,000) and (1995, 7,404,000) where the first coordinate is the x value and the second is the unemployment number. The average change is the slope of the line and is given by
m = (7,404,000 - 7,637,000)/(1995 -1980)
You can solve part b by determining the equation for the line. This is the equation
y-7,404,000=m(x-1995) or y = mx - m*1995 + 7,404,000
Use the m you found for part a. Then put in x=2055 and find y.
Thanks Roger, but I need to have a simpliar answer than that. I appreciate your trying however.
Ok, well I don't know wheher you're expected to know algebra for this course or not, but this question involves knowlege of the equations for lines.
The data is
Year Unemployed
1980 7,637,000
1995 7,404,000
In a standard graph the years would be on the x-axis and the unemployed numbers would be on the y-axis. The two data points above will determine a line. The slope of the line is
m = (7,404,000 - 7,637,000)/(1995 - 1980) = -233000/15 = -15533.33
That is the average rate of change in the unemployed number each year.
The equation for the line through the two points is given by
y - 7,404,000 =m(x - 1995) or
(1) y = -15533*x + 38392335
To determine the unemployment rate in 2055, set x=2055 and solve for y.
I can't make this any simpler without doing it completely (and I've already done part a).
I apologize for any confusion caused earlier. Let's approach the problem in a more simplified way.
a. To find the average change in unemployment for each of the 15 years between 1980 and 1995, you can subtract the initial unemployment value from the final unemployment value and divide it by the number of years.
Average change = (Final value - Initial value) / Number of years
Average change = (7,404,000 - 7,637,000) / 15
Average change = -22,200
Therefore, the average change in unemployment for each of the 15 years is -22,200.
b. Given the average change in unemployment per year, we can estimate the number of unemployed Americans in 2055 if the decline continues at the same rate.
To do this, we need to determine the equation for the line that represents the decline in unemployment. We can then substitute the year 2055 into the equation to find the corresponding unemployment value.
Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1)
where y is the unemployment value, x is the year, m is the average change in unemployment per year, and (x1, y1) is any point on the line.
Let's use the point (1995, 7,404,000):
y - 7,404,000 = -22,200(x - 1995)
Simplifying the equation:
y - 7,404,000 = -22,200x + 43,930,000
y = -22,200x + 51,334,000
Now, substitute x = 2055 into the equation:
y = -22,200(2055) + 51,334,000
y = -45,861,000 + 51,334,000
y = 5,473,000
Therefore, if the decline in unemployment continues at the same rate, it is estimated that there will be 5,473,000 unemployed Americans in the year 2055.