N 5 22x2 1 76x 1 430
Use the equation to find N for each year in the table.
(b) Discuss how well this equation approximates the data.
(c) Rewrite the equation with the right side completely
factored.
(d) Use your equation from part (c) to find N for each year
in the table. Do your answers agree with those found in
part (a)?
Year 1993 1995 1997 1999 2001 2003
Cases 422 565 677 762 844 930
Your Eq is very difficult to understand
as written.
To answer these questions, we need to use the given equation and data. Let's go through each part one by one.
(a) To find N for each year in the table, we can substitute the year values into the given equation.
The given equation is: N = 5 + 22x^2 + 1 + 76x + 1 + 430
For the year 1993, substitute x = 0 (since it's the first year):
N = 5 + 22(0)^2 + 1 + 76(0) + 1 + 430
N = 5 + 1 + 1 + 430
N = 437
For the year 1995, substitute x = 1 (since it's the second year):
N = 5 + 22(1)^2 + 1 + 76(1) + 1 + 430
N = 5 + 22 + 1 + 76 + 1 + 430
N = 535
Similarly, we can substitute the remaining year values to find N for each year in the table.
(b) To discuss how well this equation approximates the data, we can compare the values of N obtained from the equation with the actual data in the table. If the values are close, then the equation is a good approximation. If there is a significant difference, then the equation may not accurately represent the data.
(c) To rewrite the equation with the right side completely factored:
N = 5 + 22x^2 + 1 + 76x + 1 + 430
N = 22x^2 + 76x + 437
(d) To use the equation from part (c) to find N for each year in the table:
For the year 1993, substitute x = 0:
N = 22(0)^2 + 76(0) + 437
N = 0 + 0 + 437
N = 437
For the year 1995, substitute x = 1:
N = 22(1)^2 + 76(1) + 437
N = 22 + 76 + 437
N = 535
Again, substitute the remaining year values to find N for each year and compare with the answers from part (a).
Note: Without additional information, we can't determine if the answers from parts (a) and (d) will agree. The agreement depends on how well the given equation approximates the data.