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 .

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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.

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Question 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final…

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

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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

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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

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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

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Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

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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.

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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.

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