The phase line and also to discuss the reasonableness of the given model d P d t = r P ( M − P ) ( P − m ) for the growth rate of the deer population.

Question

Want to see the full answer?

Answer 1

Question

Chapter 9.4, Problem 14E

(a)

To determine

To sketch: The phase line and also to discuss the reasonableness of the given model dPdt=rP(M−P)(P−m) for the growth rate of the deer population.

(b)

To determine

The way in which the model differs from the logistic model dPdt=rP(M−P) and also to determine whether is it more or less reasonable than the logistic model.

(c)

To determine

To show: The value of limt→∞P(t)=M, if P>M for all t.

(d)

To determine

The consequences if P<m for all t.

(e)

To determine

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of P and also to determine the number of permits to be issued.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.

(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =

(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0

Answer 2

Question

Chapter 9.4, Problem 14E

(a)

To determine

To sketch: The phase line and also to discuss the reasonableness of the given model dPdt=rP(M−P)(P−m) for the growth rate of the deer population.

(b)

To determine

The way in which the model differs from the logistic model dPdt=rP(M−P) and also to determine whether is it more or less reasonable than the logistic model.

(c)

To determine

To show: The value of limt→∞P(t)=M, if P>M for all t.

(d)

To determine

The consequences if P<m for all t.

(e)

To determine

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of P and also to determine the number of permits to be issued.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 9.4, Problem 14E

(a)

To determine

To sketch: The phase line and also to discuss the reasonableness of the given model dPdt=rP(M−P)(P−m) for the growth rate of the deer population.

(b)

To determine

The way in which the model differs from the logistic model dPdt=rP(M−P) and also to determine whether is it more or less reasonable than the logistic model.

(c)

To determine

To show: The value of limt→∞P(t)=M, if P>M for all t.

(d)

To determine

The consequences if P<m for all t.

(e)

To determine

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of P and also to determine the number of permits to be issued.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 9.4, Problem 14E

(a)

To determine

To sketch: The phase line and also to discuss the reasonableness of the given model dPdt=rP(M−P)(P−m) for the growth rate of the deer population.

(b)

To determine

The way in which the model differs from the logistic model dPdt=rP(M−P) and also to determine whether is it more or less reasonable than the logistic model.

(c)

To determine

To show: The value of limt→∞P(t)=M, if P>M for all t.

(d)

To determine

The consequences if P<m for all t.

(e)

To determine

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of P and also to determine the number of permits to be issued.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 9.4, Problem 14E

(a)

To determine

To sketch: The phase line and also to discuss the reasonableness of the given model dPdt=rP(M−P)(P−m) for the growth rate of the deer population.

(b)

To determine

The way in which the model differs from the logistic model dPdt=rP(M−P) and also to determine whether is it more or less reasonable than the logistic model.

(c)

To determine

To show: The value of limt→∞P(t)=M, if P>M for all t.

(d)

To determine

The consequences if P<m for all t.

(e)

To determine

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of P and also to determine the number of permits to be issued.

Answer 6

Chapter 9.4, Problem 14E

(a)

To determine

To sketch: The phase line and also to discuss the reasonableness of the given model dPdt=rP(M−P)(P−m) for the growth rate of the deer population.

Answer 7

Chapter 9.4, Problem 14E

(a)

To determine

To sketch: The phase line and also to discuss the reasonableness of the given model dPdt=rP(M−P)(P−m) for the growth rate of the deer population.

Answer 8

(b)

To determine

The way in which the model differs from the logistic model dPdt=rP(M−P) and also to determine whether is it more or less reasonable than the logistic model.

Answer 9

(b)

To determine

The way in which the model differs from the logistic model dPdt=rP(M−P) and also to determine whether is it more or less reasonable than the logistic model.

Answer 10

(c)

To determine

To show: The value of limt→∞P(t)=M, if P>M for all t.

Answer 11

(c)

To determine

To show: The value of limt→∞P(t)=M, if P>M for all t.

Answer 12

(d)

To determine

The consequences if P<m for all t.

Answer 13

(d)

To determine

The consequences if P<m for all t.

Answer 14

(e)

To determine

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of P and also to determine the number of permits to be issued.

Answer 15

(e)

To determine

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of P and also to determine the number of permits to be issued.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 19

Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - In Exercises 7–12, write an equivalent first-order...Ch. 9.1 - Prob. 10E

The phase line and also to discuss the reasonableness of the given model d P d t = r P ( M − P ) ( P − m ) for the growth rate of the deer population.

Concept explainers

Videos

To sketch: The phase line and also to discuss the reasonableness of the given model dPdt=rP(M−P)(P−m) for the growth rate of the deer population.

The way in which the model differs from the logistic model dPdt=rP(M−P) and also to determine whether is it more or less reasonable than the logistic model.

To show: The value of limt→∞P(t)=M, if P>M for all t.

The consequences if P<m for all t.

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of P and also to determine the number of permits to be issued.

Want to see the full answer?

Chapter 9 Solutions