The price function p ( t ) = 4 − C e − 0.2 t is the general solution of the differential equation d p d t = 0.8 − 0.2 p and evaluate the equilibrium price p ¯ .

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Answer 1

Question

Chapter 9.1, Problem 62E

(A)

To determine

To show: The price function p(t)=4−Ce−0.2t is the general solution of the differential equation dpdt=0.8−0.2p and evaluate the equilibrium price p¯.

(B)

To determine

To graph: The particular solutions satisfying the initial conditions p(0)=2 and p(0)=8.

(C)

To determine

To discuss: The long-term behavior of the price of the product.

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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.

Answer 2

Question

Chapter 9.1, Problem 62E

(A)

To determine

To show: The price function p(t)=4−Ce−0.2t is the general solution of the differential equation dpdt=0.8−0.2p and evaluate the equilibrium price p¯.

(B)

To determine

To graph: The particular solutions satisfying the initial conditions p(0)=2 and p(0)=8.

(C)

To determine

To discuss: The long-term behavior of the price of the product.

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Answer 3

Question

Chapter 9.1, Problem 62E

(A)

To determine

To show: The price function p(t)=4−Ce−0.2t is the general solution of the differential equation dpdt=0.8−0.2p and evaluate the equilibrium price p¯.

(B)

To determine

To graph: The particular solutions satisfying the initial conditions p(0)=2 and p(0)=8.

(C)

To determine

To discuss: The long-term behavior of the price of the product.

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Answer 4

Question

Chapter 9.1, Problem 62E

(A)

To determine

To show: The price function p(t)=4−Ce−0.2t is the general solution of the differential equation dpdt=0.8−0.2p and evaluate the equilibrium price p¯.

(B)

To determine

To graph: The particular solutions satisfying the initial conditions p(0)=2 and p(0)=8.

(C)

To determine

To discuss: The long-term behavior of the price of the product.

Expert Solution & Answer

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Answer 5

Chapter 9.1, Problem 62E

(A)

To determine

To show: The price function p(t)=4−Ce−0.2t is the general solution of the differential equation dpdt=0.8−0.2p and evaluate the equilibrium price p¯.

(B)

To determine

To graph: The particular solutions satisfying the initial conditions p(0)=2 and p(0)=8.

(C)

To determine

To discuss: The long-term behavior of the price of the product.

Answer 6

Chapter 9.1, Problem 62E

(A)

To determine

To show: The price function p(t)=4−Ce−0.2t is the general solution of the differential equation dpdt=0.8−0.2p and evaluate the equilibrium price p¯.

Answer 7

Chapter 9.1, Problem 62E

(A)

To determine

To show: The price function p(t)=4−Ce−0.2t is the general solution of the differential equation dpdt=0.8−0.2p and evaluate the equilibrium price p¯.

Answer 8

(B)

To determine

To graph: The particular solutions satisfying the initial conditions p(0)=2 and p(0)=8.

Answer 9

(B)

To determine

To graph: The particular solutions satisfying the initial conditions p(0)=2 and p(0)=8.

Answer 10

(C)

To determine

To discuss: The long-term behavior of the price of the product.

Answer 11

(C)

To determine

To discuss: The long-term behavior of the price of the product.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MP Ch. 9.1 - Prob. 3MP Ch. 9.1 - Prob. 4MP Ch. 9.1 - Prob. 5MP Ch. 9.1 - Prob. 1ED Ch. 9.1 - Prob. 2ED Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E

The price function p ( t ) = 4 − C e − 0.2 t is the general solution of the differential equation d p d t = 0.8 − 0.2 p and evaluate the equilibrium price p ¯ .

Solution Summary: The author explains how the price function p(t)=4-Ce-0.2t is the general solution of the differential equation and evaluates the equilibrium price.

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To show: The price function p(t)=4−Ce−0.2t is the general solution of the differential equation dpdt=0.8−0.2p and evaluate the equilibrium price p¯.

To graph: The particular solutions satisfying the initial conditions p(0)=2 and p(0)=8.

To discuss: The long-term behavior of the price of the product.

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