The carrying capacity and intrinsic rate of the logistic equation d N d t = − N 2 + N with the initial condition N ( 0 ) = 0.5 .

Question

Want to see the full answer?

Answer 1

Question

Chapter 10.6, Problem 4E

(a)

To determine

The carrying capacity and intrinsic rate of the logistic equation dNdt=−N2+N with the initial condition N(0)=0.5.

(b)

To determine

To graph: The function dNdt=−N2+N versus N in an Nz-plane.

(c)

To determine

To graph: The constant solution of dNdt=−N2+N in tN-plane and place a dash line where the concavity of solution may change.

(d)

To determine

To graph: The solution curve of the differential equation dNdt=−N2+N corresponding to the initial condition N(0)=0.5.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Total marks 15 3. (i) Let FRN Rm be a mapping and x = RN is a given point. Which of the following statements are true? Construct counterex- amples for any that are false. (a) If F is continuous at x then F is differentiable at x. (b) If F is differentiable at x then F is continuous at x. If F is differentiable at x then F has all 1st order partial (c) derivatives at x. (d) If all 1st order partial derivatives of F exist and are con- tinuous on RN then F is differentiable at x. [5 Marks] (ii) Let mappings F= (F1, F2) R³ → R² and G=(G1, G2) R² → R² : be defined by F₁ (x1, x2, x3) = x1 + x², G1(1, 2) = 31, F2(x1, x2, x3) = x² + x3, G2(1, 2)=sin(1+ y2). By using the chain rule, calculate the Jacobian matrix of the mapping GoF R3 R², i.e., JGoF(x1, x2, x3). What is JGOF(0, 0, 0)? (iii) [7 Marks] Give reasons why the mapping Go F is differentiable at (0, 0, 0) R³ and determine the derivative matrix D(GF)(0, 0, 0). [3 Marks]

5. (i) Let f R2 R be defined by f(x1, x2) = x² - 4x1x2 + 2x3. Find all local minima of f on R². (ii) [10 Marks] Give an example of a function f: R2 R which is not bounded above and has exactly one critical point, which is a minimum. Justify briefly Total marks 15 your answer. [5 Marks]

Total marks 15 4. : Let f R2 R be defined by f(x1, x2) = 2x²- 8x1x2+4x+2. Find all local minima of f on R². [10 Marks] (ii) Give an example of a function f R2 R which is neither bounded below nor bounded above, and has no critical point. Justify briefly your answer. [5 Marks]

Answer 2

Question

Chapter 10.6, Problem 4E

(a)

To determine

The carrying capacity and intrinsic rate of the logistic equation dNdt=−N2+N with the initial condition N(0)=0.5.

(b)

To determine

To graph: The function dNdt=−N2+N versus N in an Nz-plane.

(c)

To determine

To graph: The constant solution of dNdt=−N2+N in tN-plane and place a dash line where the concavity of solution may change.

(d)

To determine

To graph: The solution curve of the differential equation dNdt=−N2+N corresponding to the initial condition N(0)=0.5.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 10.6, Problem 4E

(a)

To determine

The carrying capacity and intrinsic rate of the logistic equation dNdt=−N2+N with the initial condition N(0)=0.5.

(b)

To determine

To graph: The function dNdt=−N2+N versus N in an Nz-plane.

(c)

To determine

To graph: The constant solution of dNdt=−N2+N in tN-plane and place a dash line where the concavity of solution may change.

(d)

To determine

To graph: The solution curve of the differential equation dNdt=−N2+N corresponding to the initial condition N(0)=0.5.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 10.6, Problem 4E

(a)

To determine

The carrying capacity and intrinsic rate of the logistic equation dNdt=−N2+N with the initial condition N(0)=0.5.

(b)

To determine

To graph: The function dNdt=−N2+N versus N in an Nz-plane.

(c)

To determine

To graph: The constant solution of dNdt=−N2+N in tN-plane and place a dash line where the concavity of solution may change.

(d)

To determine

To graph: The solution curve of the differential equation dNdt=−N2+N corresponding to the initial condition N(0)=0.5.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 10.6, Problem 4E

(a)

To determine

The carrying capacity and intrinsic rate of the logistic equation dNdt=−N2+N with the initial condition N(0)=0.5.

(b)

To determine

To graph: The function dNdt=−N2+N versus N in an Nz-plane.

(c)

To determine

To graph: The constant solution of dNdt=−N2+N in tN-plane and place a dash line where the concavity of solution may change.

(d)

To determine

To graph: The solution curve of the differential equation dNdt=−N2+N corresponding to the initial condition N(0)=0.5.

Answer 6

Chapter 10.6, Problem 4E

(a)

To determine

The carrying capacity and intrinsic rate of the logistic equation dNdt=−N2+N with the initial condition N(0)=0.5.

Answer 7

Chapter 10.6, Problem 4E

(a)

To determine

The carrying capacity and intrinsic rate of the logistic equation dNdt=−N2+N with the initial condition N(0)=0.5.

Answer 8

(b)

To determine

To graph: The function dNdt=−N2+N versus N in an Nz-plane.

Answer 9

(b)

To determine

To graph: The function dNdt=−N2+N versus N in an Nz-plane.

Answer 10

(c)

To determine

To graph: The constant solution of dNdt=−N2+N in tN-plane and place a dash line where the concavity of solution may change.

Answer 11

(c)

To determine

To graph: The constant solution of dNdt=−N2+N in tN-plane and place a dash line where the concavity of solution may change.

Answer 12

(d)

To determine

To graph: The solution curve of the differential equation dNdt=−N2+N corresponding to the initial condition N(0)=0.5.

Answer 13

(d)

To determine

To graph: The solution curve of the differential equation dNdt=−N2+N corresponding to the initial condition N(0)=0.5.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 17

Ch. 10.1 - Show that any function of the form y=Aet3/3, where...Ch. 10.1 - If the function f(t) is a solution of the...Ch. 10.1 - Prob. 3CYU Ch. 10.1 - Show that the function f(t)=32et212 is a solution...Ch. 10.1 - Show that the function f(t)=t212 is a solution of...Ch. 10.1 - Show that the function f(t)=5e2t satisfies...Ch. 10.1 - Show that the function f(t)=(et+1)1 satisfies...Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Is the constant function f(t)=3 a solution of the...

The carrying capacity and intrinsic rate of the logistic equation d N d t = − N 2 + N with the initial condition N ( 0 ) = 0.5 .

Solution Summary: The author compares the logistic equation dNt=-n2+N with the initial condition N(0)=0.5.

Concept explainers

Videos

The carrying capacity and intrinsic rate of the logistic equation dNdt=−N2+N with the initial condition N(0)=0.5.

To graph: The function dNdt=−N2+N versus N in an Nz-plane.

To graph: The constant solution of dNdt=−N2+N in tN-plane and place a dash line where the concavity of solution may change.

To graph: The solution curve of the differential equation dNdt=−N2+N corresponding to the initial condition N(0)=0.5.

Want to see the full answer?

Chapter 10 Solutions