The funding f t in $ millions for a drug rehabilitation center is given in the table for selected years t . a. Use regression to find a quadratic function to model the data. b. During what year is the funding the least? Round to the nearest year. c. What is the minimum yearly amount of funding received? Round to the nearest million.
The funding f t in $ millions for a drug rehabilitation center is given in the table for selected years t . a. Use regression to find a quadratic function to model the data. b. During what year is the funding the least? Round to the nearest year. c. What is the minimum yearly amount of funding received? Round to the nearest million.
Solution Summary: The author explains the quadratic expression using the regression method to model the given data.
A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
Elementary Statistics: Picturing the World (7th Edition)
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