SOLUTION: 2. According to the New York Times, the number of people receiving food stamps increased in the early 90’s, but then decreased later in the 90’s. Observe the table below.
Y
Algebra ->
Functions
-> SOLUTION: 2. According to the New York Times, the number of people receiving food stamps increased in the early 90’s, but then decreased later in the 90’s. Observe the table below.
Y
Log On
Question 1137344: 2. According to the New York Times, the number of people receiving food stamps increased in the early 90’s, but then decreased later in the 90’s. Observe the table below.
Year 1990 1992 1994 1996 1998
Average Monthly Participants
(millions of people) 20.0 25.2 27.3 25.4 19.8
a. Let x = 0 correspond to 1990. Use the regression capabilities of your calculator to determine the equation (linear or quadratic) that best models the data. Explain why you selected the one you did.
b. Use the regression equation to determine the average number of monthly
c. participants in the food stamp program in 1995:
d. Use the regression equation to find when the average number of monthly participants in the food stamp program is exactly 25 million?
e. What was the greatest number of monthly participants in the food stamp program and when did it occur?
f. Identify and interpret the meaning of the vertical intercept.
g. Identify and interpret the horizontal intercepts. Discuss the reasonableness of these values in the context of the problem.
h. State the practical domain and range in the context of the problem.
You can put this solution on YOUR website! Linear=23.58-0.01x with an R^2 of about 0,, which is essentially no correlation at all
Quadratic is -0.457x^2+3.647x+19.92 with an R^2 of 0.999, which is almost no deviation at all from a quadratic model (not as surprising given few data points and a rise and a fall).
-0.457x^2+3.647x+19.92=25.0
-0.457x^2+3.647x-5.08=0
x+(-1/0.914)(-3.647 +/- sqrt 4.01); sqrt is 2
x=(-1/.914)(-5.647)=6.18 or about 2 months into 1997 it was 25 million
x=(-1/.914)(-1.647)=1.80 or about 10 months into 1992 it was 25 million
in 1995, it was 26.73, letting x=5
The y-intercept is the number in 1990.
The x-intercept would be further out in time or further back in time and might correspond to when the program began or not. It is beyond the capability of the model.
Practical domain is within 1990-1998
practical range is between 19.8 and 27.3, since we have no further data to support anything further.
Maximum is when x=-b/2a or 3.99
f(x)=27.19 at almost exactly 4.0, despite the actual data's showing 27.3 at 4.0
