# Section 6- 5 Equations of Change Graphical Solutions

Business

Q 1Q 1

Equilibrium or steady-state solutions for an equation of change are solutions that remain constant.

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True False

True

Q 2Q 2

Equilibrium or steady-state solutions for an equation of change occur where the rate of change is 0.

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True False

True

Q 3Q 3

The carrying capacity is an equilibrium solution for the equation of change for logistic growth.

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True False

True

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True False

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True False

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True False

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True False

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Q 11Q 11

Find the equilibrium solution of the equation of change .Round your answer to two decimal places.
A)
B)
C)
D)

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Q 12Q 12

Find the equilibrium solutions of the equation of change .Round your answers to two decimal places, if necessary.
A) and
B) and
C) and
D) and

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Q 14Q 14

Find the equilibrium solutions of the equation of change .Round your answer to two decimal places, if necessary.
A) and
B) and
C) and
D) and

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Q 16Q 16

Find the equilibrium solutions of the equation of change .Round your answer to two decimal places, if necessary.
A) and
B) and
C) and
D) and

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Q 17Q 17

Find the equilibrium solution of the equation of change .Round your answer to two decimal places, if nessary.
A)
B)
C)
D)

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Q 18Q 18

Find the equilibrium solution of the equation of change .Consider only positive values of x.Round your answer to two decimal places, if nessary.
A)
B)
C)
D)

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Q 19Q 19

Find the equilibrium solution of the equation of change .Consider only positive values of x.
A)
B)
C)
D)

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Q 20Q 20

The function satisfies the equation of change .For what values of f is the graph of f versus x increasing? Round your answer to two decimal places.
A)
B)
C)
D)

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Q 21Q 21

The function satisfies the equation of change .For what values of f is the graph of f versus x increasing? Round your answer to two decimal places, if necessary.
A)
B)
C)
D)

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Q 22Q 22

The function satisfies the equation of change .For what values of f is the graph of f versus x increasing?
A)
B)
C)
D)

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Q 23Q 23

The function satisfies the equation of change .For what value of f is f increasing at the fastest rate? Round your answer to two decimal places, if necessary.
A)
B)
C)
D)

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Q 24Q 24

The function satisfies the equation of change .For what value of f is f increasing at the fastest rate?
A)
B)
C)
D)

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Q 25Q 25

The function satisfies the equation of change .For what values of f is the graph of f versus x decreasing?
A)
B)
C)
D)

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Q 26Q 26

If is an equilibrium solution of an equation of change involving , what is the value of when ?
A) 0
B) 5
C) -5
D) None of the above

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Q 27Q 27

Consider the equation of change .What can you say about the graph of f versus x when ?
A) The graph is increasing.
B) The graph is decreasing.
C) The graph reaches a maximum.
D) The graph reaches a minimum.

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Multiple Choice

Q 28Q 28

Consider the equation of change .What can you say about the graph of f versus x when ?
A) The graph is increasing.
B) The graph is decreasing.
C) The graph reaches a maximum.
D) The graph reaches a minimum.

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Q 29Q 29

The amount L, in liters, of liquid remaining in a tank after t hours satisfies the equation of change .How much liquid is in the tank after a long time?
A) 6 liters
B) 42 liters
C) 1.17 liters
D) 7 liters

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Q 30Q 30

The amount L, in liters, of liquid remaining in a tank after t hours satisfies the equation of change .What is happening to the liquid in the tank when there are 53 liters present?
A) The amount of liquid is at a minimum.
B) The amount of liquid in increasing.
C) The amount of liquid is deceasing.
D) The amount of liquid is at a maximum.

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Q 31Q 31

The amount L, in liters, of liquid remaining in a tank after t hours satisfies the equation of change .What is happening to the liquid in the tank when there are 31 liters present?
A) The amount of liquid is at a minimum.
B) The amount of liquid in increasing.
C) The amount of liquid is deceasing.
D) The amount of liquid is at a maximum.

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Multiple Choice

Q 32Q 32

A certain population grows according to .What is the carrying capacity of the environment for this particular population? Round your answer to two decimal places, if necessary.
A) 351
B) 0.03
C) 11
D) 11,700

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Q 33Q 33

A certain population grows according to .At a certain time the population is 698 individuals.What can be said about the population at this time?
A) The population is increasing.
B) The population is decreasing.
C) The population has reached a maximum value.
D) The population has reached a minimum value.

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Q 34Q 34

A certain population grows according to .At a certain time the population is 1,140 individuals.What can be said about the population at this time?
A) The population is increasing.
B) The population is decreasing.
C) The population has reached a maximum value.
D) The population has reached a minimum value.

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Multiple Choice

Q 35Q 35

The weight w, in pounds, of a certain animal at age t years satisfies the equation of change .For what values of the weight w is the animal losing weight? Round your answer to two decimal places.
A) pounds
B) pounds
C) 2.90 pounds
D) None of the above

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Multiple Choice

Q 36Q 36

The weight w, in pounds of a certain animal at age t years satisfies the equation of change .At what weight is the animal growing the fastest? Round your answer to two decimal places.
A) 0.47 pounds
B) 2.13 pounds
C) 1.06 pounds
D) None of the above

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Multiple Choice

Q 37Q 37

A certain population grows according to an equation of change.What can be said of population growth when the population level is at a steady state solution of the equation of change?
A) The population is stable--neither increasing nor decreasing.
B) The population is increasing.
C) The population is decreasing.
D) There is not sufficient information to determine how population grows.

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Multiple Choice

Q 38Q 38

The weight w of a certain animal satisfies an equation of change.At a specific weight, the equation of change indicates that is positive.What can you conclude about how the animal's weight can be expected to change?
A) The weight will stay the same.
B) The animal will gain weight.
C) The animal will lose weight.
D) The weight is at a minimum value.

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Multiple Choice

Q 39Q 39

The weight w of a certain animal satisfies an equation of change.At a specific weight, the equation of change indicates that is negative.What can you conclude about how the animal's weight can be expected to change?
A) The weight will stay the same.
B) The animal will gain weight.
C) The animal will lose weight.
D) The weight is at a maximum value.

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