find the function that relates the unemployment rate as function the DJIA.

Question

The unemployment rate in January 2010 was 9.9%, and the unemployment rate in April

2014 was 6.3% (http://data.bls.gov/timeseries/LNS14000000). The Dow Jones Industrial

Average (DJIA) was 10,428.05 on January 1, 2010, and 16,532.84 on April 1, 2014.

Assuming that unemployment rate and the DJIA are linearly related, find the function

that relates the unemployment rate as function the DJIA.

Answer 1

It would be helpful to have some idea of what the variables you require would be in this question. Nevertheless, I will make an attempt.

 

Let t be the time in months, with t = 0 corresponding to January, 2010 and t = 52 corresponding to April 1, 2014.

 

Let y = the unemployment rate as a function of t. So, you are given y = 9.9 when t = 0 and y = 6.3 when t = 52. This produces the ordered pairs (0,9.9) and (52,6.3). They will pass through a line with slope m₁ = (6.3 - 9.9)/(52 - 0) = -9/130.

 

Let x = the DJIA as a function of t. You are given x = 10428.05 when t = 0 and x = 16532.84 when t = 52. This also produces two ordered pairs (0, 10428.05) and (52, 16532.84). The also pass through a line with slope m₂ = (16532.84 - 10428.05)/52 = 6104.79/52 = 117.4.

 

The equation for y as a function of t is y = -9/130 t + 9.9; the equation for x as a function of t is x = 117.4t + 10428.05.

 

Now at this point (or even earlier), you have two options. Since you know that both x and y are linear equations in t, you also know that y will be a linear equation in x. Here are two ways to find that function.

 

1) Solve x = 117.4t + 10428.05 for t in terms of x, plug it into the equation for y in terms of t, and then simplify. This is much harder than the second method.

 

2) Think of the ordered pairs (9.9, 10428.05) and (6.3, 16532.84) as points on the line with graph the desired equation. Find the slope of this line and use the point-slope equation to find its equation.

 

In fact, you could proceed directly to 2) if you realize that all equations in this problem are linear and save a lot of reading. Sorry, but I cannot resist showing you a little about planning ahead before asking someone for help with a problem, since I didn't.

 

Hint: The slope m = -1695.78. You should be able to finish from here.

 

You can check your answer by plugging in the original data and verifying the equation is satisfied.