(a) To sketch: The slope field of d P d t = − k P ( 1 − P B ) .

Question

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Answer 1

Question

Chapter 9.4, Problem 16E

To determine

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

To determine

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

To determine

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

To determine

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.

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Answer 2

Question

Chapter 9.4, Problem 16E

To determine

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

To determine

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

To determine

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

To determine

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 9.4, Problem 16E

To determine

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

To determine

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

To determine

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

To determine

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 9.4, Problem 16E

To determine

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

To determine

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

To determine

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

To determine

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 9.4, Problem 16E

To determine

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

To determine

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

To determine

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

To determine

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.

Answer 6

Chapter 9.4, Problem 16E

To determine

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

Answer 7

Chapter 9.4, Problem 16E

To determine

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

Answer 8

To determine

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

Answer 9

To determine

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

Answer 10

To determine

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

Answer 11

To determine

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

Answer 12

To determine

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.

Answer 13

To determine

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 4PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E

(a) To sketch: The slope field of d P d t = − k P ( 1 − P B ) .

Solution Summary: The author illustrates the slope field of the logistic equation dPt=-kP

Concept explainers

Videos

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.

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Chapter 9 Solutions

(a) To sketch: The slope field of d P d t = − k P ( 1 − P B ) .

Solution Summary: The author illustrates the slope field of the logistic equation dPt=-kP

Concept explainers

Videos

(a) To sketch: The slope field of dPdt=−kP(1−PB).

(b) To prove: P(0)>B if C>1 and 0<P(0)<B if C<0.

(c) To show: The equation dPdt=−kP(1−PB) models an extinction-explosion population.

(d) To show: P=0 is a stable equilibrium and P=B is an unstable equilibrium.

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Chapter 9 Solutions

(a)

To sketch:

The slope field of dPdt=−kP(1−PB).

(b)

To prove:

P(0)>B if C>1 and 0<P(0)<B if C<0.

(c)

To show:

The equation dPdt=−kP(1−PB) models an extinction-explosion population.

(d)

To show:

P=0 is a stable equilibrium and P=B is an unstable equilibrium.