, TESTBANK For Elementary Differential
Equations 12e Boyce
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,Elementary Differential Equations, 12e (Boyce)
Chapter 1 Introduction
1) A portion of the direction field for the differential equation = f(y) is shown below:
The dotted horizontal line has equation y = 18. Fill in the following chart to indicate the
behavior as t → ∞ of the solution y(t) of the differential equation corresponding to each initial
condition .
Approaches
Initial the line Approaches Tends towards Tends towards
Condition
the x-axis ∞ ∞
36
9
0
18
Answer:
Approaches
Initial the line Approaches Tends towards Tends towards
Condition
the x-axis ∞ ∞
36 X
9 X
0 X
18 X
Type: ES Var: 1
1
,2) A portion of the direction field for the differential equation = f(y) is shown below:
The dotted horizontal line has equation y = -7. Which of the following statements are true?
Select all that apply.
A) y(t) = 0 is the solution to the initial-value problem = f(y), y(0) = 0.
B) y(t) = -7 is the only equilibrium solution.
C) There is no solution of the initial-value problem = f(y), y(0) = when = -7.
D) Every solution curve y(t) is increasing toward a negative limit as t → ∞.
E) Every solution curve y(t) tends towards -7 as t → ∞.
F) F(y) cannot be a linear function of y.
Answer: B, E, F
Type: MC Var: 1
3) Which of the following pairs of values of A and B are such that all solutions of the differential
equation = Ay + B are such that y(t) = 7? Select all that apply.
A) A = -2, B = 14
B) A = -7, B = 1
C) A = -1, B = 7
D) A = 1, B = -7
E) A = -3, B = 21
F) A = -2, B = -14
G) A = 2, B = -14
Answer: A, C, E
Type: MC Var: 1
2
,4) Which of the following pairs of values of A and B are such that all solutions of the differential
equation = Ay + B diverge away from the line y = 10 as t → ∞? Select all that apply.
A) A = -2, B = 20
B) A = 3, B = -30
C) A = 1, B = -10
D) A = -1, B = 10
E) A = -2, B = -20
F) A = 10, B = -1
G) A = 2, B = -20
Answer: B, C, G
Type: MC Var: 1
3
,5) Eight differential equations and four slope fields are given below.
(A) =1- (B) =t-1 (C) =1-y
(D) =1-t (E) = - (F) = -
(G) =1+y (H) = -1
(i) (ii)
(iii) (iv)
Which of the following are the zero isoclines for the differential equation in (A)? Select all that
apply.
A) y = 0
B) y = 1
C) y = -1
D) y = t
E) y = -t
Answer: B, C
Type: MC Var: 1
4
,6) Eight differential equations and four slope fields are given below.
(A) =1- (B) =t-1 (C) =1-y
(D) =1-t (E) = - (F) = -
(G) =1+y (H) = -1
(i) (ii)
(iii) (iv)
Determine the differential equation that corresponds to each slope field. Fill in the correct letter
next to each number below:
Slope Field Differential Equation
(i)
(ii)
(iii)
(iv)
5
,Answer:
Slope Field Differential Equation
(i) B
(ii) C
(iii) H
(iv) F
Type: ES Var: 1
7) A pond initially contains 70,000 gallons of water and an unknown amount of pesticide.
Water containing 0.07 grams of pesticide per gallon flows into the pond at a rate of 360 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
Which of these is the differential equation for the amount of pesticide, P(t), in the pond at any
time t?
A) = 0.07 - P(t)
B) = 25.2 - P(t)
C) = P(t) - 360
D) = 360
Answer: B
Type: MC Var: 1
8) A pond initially contains 150,000 gallons of water and an unknown amount of pesticide.
Water containing 0.08 grams of pesticide per gallon flows into the pond at a rate of 400 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
How much pesticide will be in the pond after a very long time? ________ grams.
Answer: 12,000 grams
Type: SA Var: 1
6
,9) A pond initially contains 70,000 gallons of water and an unknown amount of pesticide.
Water containing 0.05 grams of pesticide per gallon flows into the pond at a rate of 300 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
Which of these is the general solution of the differential equation for the amount of pesticide,
P(t), in the pond at any time t?
A) P(t) = 3500 + C
B) P(t) = +C
C) P(t) = 3500 + C
D) P(t) = +C
Answer: C
Type: MC Var: 1
10) A pond initially contains 100,000 gallons of water and an unknown amount of pesticide.
Water containing 0.07 grams of pesticide per gallon flows into the pond at a rate of 320 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
Which of these is the solution of the initial-value problem comprised of the differential equation
for the amount of pesticide, P(t), in the pond at any time t and the initial condition P(0) = ?
A) P(t) = 7000 + ( + 7000)
B) P(t) = +
C) P(t) = +( - )
D) P(t) = 7000 +
Answer: D
Type: MC Var: 1
7
, 11) A pond initially contains 120,000 gallons of water and an unknown amount of pesticide.
Water containing 0.08 grams of pesticide per gallon flows into the pond at a rate of 260 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
Which of these equations would you need to solve to find the time T (in hours) after which P(t)
is within 2% of its limiting behavior?
A) P(t) = 2∙120,000∙0.08
B) P(t) = 120,000∙0.08
C) P(t) =
D) P(t) =
Answer: B
Type: MC Var: 1
12) Newton's Law of Cooling states that the temperature of an object changes at a rate
proportional to the difference between the temperature of the object itself and the temperature of
its surroundings (typically the ambient temperature). Suppose the ambient temperature is 77°F
and the rate constant is 0.09 per minute.
Which of these is a differential equation for the temperature of the object, T(t), at any time t?
A) = -0.09(T - 77)
B) = 0.09(T - 77)
C) = -0.09T - 77
D) = -77(T - 0.09)
E) = 0.09 - 77T
Answer: A
Type: MC Var: 1
8
Equations 12e Boyce
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,Elementary Differential Equations, 12e (Boyce)
Chapter 1 Introduction
1) A portion of the direction field for the differential equation = f(y) is shown below:
The dotted horizontal line has equation y = 18. Fill in the following chart to indicate the
behavior as t → ∞ of the solution y(t) of the differential equation corresponding to each initial
condition .
Approaches
Initial the line Approaches Tends towards Tends towards
Condition
the x-axis ∞ ∞
36
9
0
18
Answer:
Approaches
Initial the line Approaches Tends towards Tends towards
Condition
the x-axis ∞ ∞
36 X
9 X
0 X
18 X
Type: ES Var: 1
1
,2) A portion of the direction field for the differential equation = f(y) is shown below:
The dotted horizontal line has equation y = -7. Which of the following statements are true?
Select all that apply.
A) y(t) = 0 is the solution to the initial-value problem = f(y), y(0) = 0.
B) y(t) = -7 is the only equilibrium solution.
C) There is no solution of the initial-value problem = f(y), y(0) = when = -7.
D) Every solution curve y(t) is increasing toward a negative limit as t → ∞.
E) Every solution curve y(t) tends towards -7 as t → ∞.
F) F(y) cannot be a linear function of y.
Answer: B, E, F
Type: MC Var: 1
3) Which of the following pairs of values of A and B are such that all solutions of the differential
equation = Ay + B are such that y(t) = 7? Select all that apply.
A) A = -2, B = 14
B) A = -7, B = 1
C) A = -1, B = 7
D) A = 1, B = -7
E) A = -3, B = 21
F) A = -2, B = -14
G) A = 2, B = -14
Answer: A, C, E
Type: MC Var: 1
2
,4) Which of the following pairs of values of A and B are such that all solutions of the differential
equation = Ay + B diverge away from the line y = 10 as t → ∞? Select all that apply.
A) A = -2, B = 20
B) A = 3, B = -30
C) A = 1, B = -10
D) A = -1, B = 10
E) A = -2, B = -20
F) A = 10, B = -1
G) A = 2, B = -20
Answer: B, C, G
Type: MC Var: 1
3
,5) Eight differential equations and four slope fields are given below.
(A) =1- (B) =t-1 (C) =1-y
(D) =1-t (E) = - (F) = -
(G) =1+y (H) = -1
(i) (ii)
(iii) (iv)
Which of the following are the zero isoclines for the differential equation in (A)? Select all that
apply.
A) y = 0
B) y = 1
C) y = -1
D) y = t
E) y = -t
Answer: B, C
Type: MC Var: 1
4
,6) Eight differential equations and four slope fields are given below.
(A) =1- (B) =t-1 (C) =1-y
(D) =1-t (E) = - (F) = -
(G) =1+y (H) = -1
(i) (ii)
(iii) (iv)
Determine the differential equation that corresponds to each slope field. Fill in the correct letter
next to each number below:
Slope Field Differential Equation
(i)
(ii)
(iii)
(iv)
5
,Answer:
Slope Field Differential Equation
(i) B
(ii) C
(iii) H
(iv) F
Type: ES Var: 1
7) A pond initially contains 70,000 gallons of water and an unknown amount of pesticide.
Water containing 0.07 grams of pesticide per gallon flows into the pond at a rate of 360 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
Which of these is the differential equation for the amount of pesticide, P(t), in the pond at any
time t?
A) = 0.07 - P(t)
B) = 25.2 - P(t)
C) = P(t) - 360
D) = 360
Answer: B
Type: MC Var: 1
8) A pond initially contains 150,000 gallons of water and an unknown amount of pesticide.
Water containing 0.08 grams of pesticide per gallon flows into the pond at a rate of 400 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
How much pesticide will be in the pond after a very long time? ________ grams.
Answer: 12,000 grams
Type: SA Var: 1
6
,9) A pond initially contains 70,000 gallons of water and an unknown amount of pesticide.
Water containing 0.05 grams of pesticide per gallon flows into the pond at a rate of 300 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
Which of these is the general solution of the differential equation for the amount of pesticide,
P(t), in the pond at any time t?
A) P(t) = 3500 + C
B) P(t) = +C
C) P(t) = 3500 + C
D) P(t) = +C
Answer: C
Type: MC Var: 1
10) A pond initially contains 100,000 gallons of water and an unknown amount of pesticide.
Water containing 0.07 grams of pesticide per gallon flows into the pond at a rate of 320 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
Which of these is the solution of the initial-value problem comprised of the differential equation
for the amount of pesticide, P(t), in the pond at any time t and the initial condition P(0) = ?
A) P(t) = 7000 + ( + 7000)
B) P(t) = +
C) P(t) = +( - )
D) P(t) = 7000 +
Answer: D
Type: MC Var: 1
7
, 11) A pond initially contains 120,000 gallons of water and an unknown amount of pesticide.
Water containing 0.08 grams of pesticide per gallon flows into the pond at a rate of 260 gallons
per hour. The mixture flows out of the pond at the same rate, so the amount of water in the
pond remains constant. Assume the pesticide is uniformly mixed throughout the pond.
Which of these equations would you need to solve to find the time T (in hours) after which P(t)
is within 2% of its limiting behavior?
A) P(t) = 2∙120,000∙0.08
B) P(t) = 120,000∙0.08
C) P(t) =
D) P(t) =
Answer: B
Type: MC Var: 1
12) Newton's Law of Cooling states that the temperature of an object changes at a rate
proportional to the difference between the temperature of the object itself and the temperature of
its surroundings (typically the ambient temperature). Suppose the ambient temperature is 77°F
and the rate constant is 0.09 per minute.
Which of these is a differential equation for the temperature of the object, T(t), at any time t?
A) = -0.09(T - 77)
B) = 0.09(T - 77)
C) = -0.09T - 77
D) = -77(T - 0.09)
E) = 0.09 - 77T
Answer: A
Type: MC Var: 1
8
