(a) The slope field of the equation

Question

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Answer 1

Question

Chapter 9.4, Problem 16E

To determine

(a)

The slope field of the equation

To determine

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

To determine

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 B$

To determine

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ an unstable equilibrium

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Answer 2

Question

Chapter 9.4, Problem 16E

To determine

(a)

The slope field of the equation

To determine

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

To determine

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 B$

To determine

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ an unstable equilibrium

Expert Solution & Answer

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Answer 3

Question

Chapter 9.4, Problem 16E

To determine

(a)

The slope field of the equation

To determine

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

To determine

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 B$

To determine

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ an unstable equilibrium

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 9.4, Problem 16E

To determine

(a)

The slope field of the equation

To determine

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

To determine

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 B$

To determine

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ an unstable equilibrium

Expert Solution & Answer

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Answer 5

Chapter 9.4, Problem 16E

To determine

(a)

The slope field of the equation

To determine

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

To determine

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 B$

To determine

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ an unstable equilibrium

Answer 6

Chapter 9.4, Problem 16E

To determine

(a)

The slope field of the equation

Answer 7

Chapter 9.4, Problem 16E

To determine

(a)

The slope field of the equation

Answer 8

To determine

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

Answer 9

To determine

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

Answer 10

To determine

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 B$

Answer 11

To determine

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 B$

Answer 12

To determine

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ an unstable equilibrium

Answer 13

To determine

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ 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. 5PQ 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

(a) The slope field of the equation

(a)

The slope field of the equation

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 < P (0) < B$ and it tends to $\infty$ after a finite amount of time if $P (0) > B$

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ an unstable equilibrium

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Chapter 9 Solutions

(a) The slope field of the equation

(a) The slope field of the equation

(b) The general solution is P(t)=B(1−ekt/C) where C is a non-zero constant. Show that P(0)>B if C>1 and 0<P(0)<B if C<0

(c) Show that Equation (8) models an “extinction-explosion” population. That is, P(t) tends to zero if the initial population satisfies 0<P(0)<B and it tends to ∞ after a finite amount of time if P(0)>B

(d) Show that P=0 is a stable equilibrium and P=B an unstable equilibrium

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Chapter 9 Solutions

(a)

The slope field of the equation

(b)

The general solution is $P (t) = \frac{B}{(1 - e^{k t} / C)}$ where $C$ is a non-zero constant. Show that $P (0) > B$ if $C > 1$ and $0 < P (0) < B$ if $C < 0$

(c)

Show that Equation (8) models an “extinction-explosion” population. That is, $P (t)$ tends to zero if the initial population satisfies $0 < P (0) < B$ and it tends to $\infty$ after a finite amount of time if $P (0) > B$

(d)

Show that $P = 0$ is a stable equilibrium and $P = B$ an unstable equilibrium