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Deck 11: Differential Equations
Full screen (f)
Question
Determine whether the function 
is a solution of the differential equation 
A) Solution
B) Not a solution
is a solution of the differential equation A) Solution
B) Not a solution
Question
Determine whether the function 
is a solution of the differential equation 
A) Not a solution
B) Solution
is a solution of the differential equation A) Not a solution
B) Solution
Question
Which of the following is a solution of the differential equation 
?
A) 
B)
C) 
D) 
E)
? A)
B)
C)
D)
E)
Question
Use the integration to find the general solution of the differential equation 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Determine whether 
is a solution of the differential equation 
A) 
and 
B) 
and 
C) 
and 
D) 
and 
E) 
and 
is a solution of the differential equation A)
and B)
and C)
and D)
and E)
and Question
Determine whether 
is a solution of the differential equation 
A) 
B) 
C) 
D)
E)
is a solution of the differential equation A)
B)
C)
D)
E)
Question
Verify that the general solution satisfies the differential equation.Then find the particular solution that satisfies the initial condition.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine whether 
is a solution of the differential equation 
A) 
and 
B)
and 
C)
and 
D) 
and 
E) 
and 
is a solution of the differential equation A)
and B)
and C)
and D)
and E)
and Question
Use the integration to find the general solution of the differential equation 
A) 
B)
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use integration to find a general solution of the differential equation.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Which of the following is a solution of the differential equation 
?
A) 
B)
C) 
D) 
E)
? A)
B)
C)
D)
E)
Question
Use the integration to find the general solution of the differential equation 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine whether the function 
is a solution of the differential equation 
A) Solution
B) Not a solution
is a solution of the differential equation A) Solution
B) Not a solution
Question
Determine whether the function 
is a solution of the differential equation 
A) Not a solution
B) Solution
is a solution of the differential equation A) Not a solution
B) Solution
Question
Some of the curves corresponding to different values of C in general solution of the differential equation 
, 
are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph. 
A)
B)
C)
D)
E)
, are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph. A)
B)
C)
D)
E)
Question
Verify that the general solution satisfies the differential equation.Then find the particular solution that satisfies the initial condition.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Some of the curves corresponding to different values of C in general solution of the differential equation 
, 
are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph.
A) 
B) 
C) 
D) 
E) 
, are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph.
A)
B)
C)
D)
E)
Question
Determine whether 
is a solution of the differential equation 
A) 
and 
B)
and 
C)
and 
D) 
and 
E) 
and 
is a solution of the differential equation A)
and B)
and C)
and D)
and E)
and Question
Use integration to find a general solution of the differential equation 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the particular solution of the differential equation 
that satisfies the initial condition 
when 
,where 
is the general solution.
A)
B)
C)
D)
E)
that satisfies the initial condition when ,where is the general solution. A)
B)
C)
D)
E)
Question
The isotope 
has a half-life of 1,599 years.Given an initial amount of 13 grams of the isotope,how many grams will remain after 1,500 years? After 15,000 years? Round your answers to four decimal places.
A) 4.7495 g, 0.0137 g
B) 2.714 g, 0.0078 g
C) 6.785 g, 0.0195 g
D) 8.142 g, 0.0234 g
E) 4.071 g,0.0273 g
has a half-life of 1,599 years.Given an initial amount of 13 grams of the isotope,how many grams will remain after 1,500 years? After 15,000 years? Round your answers to four decimal places. A) 4.7495 g, 0.0137 g
B) 2.714 g, 0.0078 g
C) 6.785 g, 0.0195 g
D) 8.142 g, 0.0234 g
E) 4.071 g,0.0273 g
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Write the the differential equation by separating the variables. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use the initial condition to find the particular solution of the differential equation. 
, 
when 
A)
B)
C)
D)
E)
, when A)
B)
C)
D)
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use the initial condition to find the particular solution of the differential equation. 
, 
when 
A) 
B) 
C) 
D) 
E) 
, when A)
B)
C)
D)
E)
Question
Use the initial condition to find the particular solution of the differential equation. 
, 
when 
A) 
B) 
C) 
D) 
E) 
, when A)
B)
C)
D)
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Write the the differential equation by separating the variables. 
A) 
B) 
C) 
D) No, the variables cannot be separated
E) 
A)
B)
C)
D) No, the variables cannot be separated
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Solve the differential equation to find velocity v as a function of time t if 
when 
The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity,friction,and air resistance. 
A) 
B) 
C) 
D) 
E) 
when The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity,friction,and air resistance. A)
B)
C)
D)
E)
Question
Use separation of variables to find the general solution of the differential equation. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find an equation of the graph that passes through the point and has the specified slope.Then graph the equation.
Point:
,
Slope:
A)
B)
C)
D)
E) None of the above
Point:
,Slope:
A)
B)
C)
D)
E) None of the above
Question
Use the initial condition to find the particular solution of the differential equation. 
, 
when 
A) 
B) 
C) 
D) 
E) 
, when A)
B)
C)
D)
E)
Question
Write the the differential equation by separating the variables. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Write the first-order linear differential equation in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve for y in two ways.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the general solution of the first-order linear differential equation.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the particular solution that satisfies the initial condition. 
; Initial Condition: 
when 
A) 
B) 
C) 
D) 
E) 
; Initial Condition: when A)
B)
C)
D)
E)
Question
Find the general solution of the first-order linear differential equation.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the particular solution of the differential equation 
passing through the point 
A)
B)
C)
D)
E)
passing through the point A)
B)
C)
D)
E)
Question
Write the first-order linear differential equation in standard form.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the general solution of the first-order linear differential equation.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the general solution of the first-order linear differential equation.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the general solution of the first-order linear differential equation.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the solution of the differential equation 
,without solving it.
A) 
B) 
C) 
D) 
E) 
,without solving it. A)
B)
C)
D)
E)
Question
Write the first-order linear differential equation in standard form.
A) 
B)
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the particular solution that satisfies the initial condition. 
; Initial Condition: 
when 
A) 
B) 
C) 
D) 
E) 
; Initial Condition: when A)
B)
C)
D)
E)
Question
Solve for y in two ways.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
A calf that weighs 75 pounds at birth gains weight at the rate 
,where w is weight in pounds and t is time in years.Use a computer algebra system to solve the differential equation for 
A)
B)
C)
D)
E)
,where w is weight in pounds and t is time in years.Use a computer algebra system to solve the differential equation for A)
B)
C)
D)
E)
Question
Find the particular solution that satisfies the initial condition. 
; Initial Condition: 
when 
A) 
B) 
C) 
D) 
E) 
; Initial Condition: when A)
B)
C)
D)
E)
Question
Find the general solution of the first-order linear differential equation.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the particular solution of the differential equation 
that satisfies the boundary condition 
A) 
B) 
C) 
D) 
E) 
that satisfies the boundary condition A)
B)
C)
D)
E)
Question
Find the solution of the differential equation 
,without solving it.
A) 
B) 
C) 
D) 
E) 
,without solving it. A)
B)
C)
D)
E)
Question
Find the particular solution that satisfies the initial condition. 
; Initial Condition: 
when 
A) 
B) 
C) 
D) 
E) 
; Initial Condition: when A)
B)
C)
D)
E)
Question
The rate of change in sales S (in thousands of units)of a new product is proportional to the difference between L and S at any time t (in years),where L is the maximum number of units of the new product available.When 
, 
Write and solve the differential equation for this sales model.
A) 
B) 
C)
D) 
E)
, Write and solve the differential equation for this sales model. A)
B)
C)
D)
E)
Question
Use this equation 
and find P if the corporation needs $120,000,000 in 8 years and the fund earns 8% interest compounded continuously.
A) $110,708,538.49
B) $10,500,538.49
C) $10,708,538.49
D) $100,708,538.49
E) $1,708,538.49
and find P if the corporation needs $120,000,000 in 8 years and the fund earns 8% interest compounded continuously. A) $110,708,538.49
B) $10,500,538.49
C) $10,708,538.49
D) $100,708,538.49
E) $1,708,538.49
Question
Question
A 200-gallon tank is full of a solution containing 55 pounds of concentrate.Starting at time t=0 ,distilled water is added to the tank at a rate of 20 gallons per minute,and the well-stirred solution is withdrawn at the same rate.Find the amount of concentrate Q in the solution as a function of t.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
A large corporation starts at time 
to invest part of its profit at a rate of P dollars per year in a fund for future expansion.Assume that the fund earns r percent interest per year compounded continuously.The rate of growth of the amount A in the fund is given by 
where 
when 
and r is in decimal form.Solve this differential equation for A as a function of t.
A) 
B)
C)
D)
E)
to invest part of its profit at a rate of P dollars per year in a fund for future expansion.Assume that the fund earns r percent interest per year compounded continuously.The rate of growth of the amount A in the fund is given by where when and r is in decimal form.Solve this differential equation for A as a function of t. A)
B)
C)
D)
E)
Question
A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate proportional to its moisture content.After 1 hour,the towel has lost 40% of its original moisture content.How long will it take the towel to lose 80% of its original moisture content?
A) 
B) 
C)
D) 
E)
A)
B)
C)
D)
E)
Question
Assume that the rate of change in y is proportional to y.Solve the resulting differential equation 
and find the particular solution that passes through the points 
, 
A) 
B) 
C) 
D) 
E) 
and find the particular solution that passes through the points , A)
B)
C)
D)
E)
Question
During a chemical reaction,a compound changes into another compound at a rate proportional to the unchanged amount y.Write the differential equation for the chemical reaction model.Find the particular solution when the initial amount of the original compound is 20 grams and the amount remaining after 1 hour is 16 grams.
A) 
, 
B) 
, 
C) 
, 
D) 
, 
E) 
, 
A)
, B)
, C)
, D)
, E)
, Question
Use the chemical reaction model described to find the amount y (in grams)as a function of time t (in hours).Then use a graphing utility to graph the function. 
grams when 
; 
grams when 
A) 
B) 
C) 
D) 
E) 
grams when ; grams when A)
B)
C)
D)
E)
Question
Use the Gompertz growth model described to find the population y as a function of time t (in years). 
when 
; 
when 
A) 
B) 
C) 
D) 
E) 
when ; when A)
B)
C)
D)
E)
Question
A medical researcher wants to determine the concentration C (in moles per liter)of a tracer drug injected into a moving fluid with flow R (in liters per minute).Solve this problem by considering a single-compartment dilution model (see figure).Assume that the fluid is continuously mixed and that the volume V (in liters)of fluid in the compartment is constant. 
If the tracer is injected instantaneously at time
,then the concentration of the fluid in the compartment begins diluting according to the differential equation 
, 
when 
(a)Solve this differential equation to find the concentration as a function of time.
(b)Find the limit of C as
A) a.
b) 1
B) a.
b) 0
C) a.
b) 2
D) a.
b) 0
E) a.
b)1
If the tracer is injected instantaneously at time
,then the concentration of the fluid in the compartment begins diluting according to the differential equation , when (a)Solve this differential equation to find the concentration as a function of time.(b)Find the limit of C as
A) a.
b) 1
B) a.
b) 0
C) a.
b) 2
D) a.
b) 0
E) a.
b)1
Question
Question
Assume that the rate of change in 
is proportional to 
Solve the resulting differential equation 
and find the particular solution that passes through the points 
, 
A) 
B) 
C) 
D) 
E) 
is proportional to Solve the resulting differential equation and find the particular solution that passes through the points , A)
B)
C)
D)
E)
Question
Use this equation 
and find A for each situation.
(a)
, 
and 
years
(b)
, 
and 
years
A) a) 685,099.00
b) 5,802,815.12
B) a) 585,099.00
b) 5,802,815.12
C) a) 685,099.00
b) 6,802,815.12
D) a) 585,099.00
b) 4,802,815.12
E)
a)485,099.00
b)5,802,815.12
and find A for each situation. (a)
, and years(b)
, and years
A) a) 685,099.00
b) 5,802,815.12
B) a) 585,099.00
b) 5,802,815.12
C) a) 685,099.00
b) 6,802,815.12
D) a) 585,099.00
b) 4,802,815.12
E)
a)485,099.00
b)5,802,815.12
Question
Use the hybrid selection model described to find the percent y (in decimal form)of the population that has the indicated characteristics as a function of time t (in generations). 
when 
; 
when 
A) 
B) 
C) 
D) 
E) 
when ; when A)
B)
C)
D)
E)
Question
Use the advertising awareness model described to find the number of people y (in millions)aware of the product as a function of time t (in years). 
when 
; 
when 
A) 
B) 
C) 
D) 
E) 
when ; when A)
B)
C)
D)
E)
Question
Assume that the rate of change in y is proportional to y.Solve the resulting differential equation 
and find the particular solution that passes through the points 
, 
A) 
B) 
C) 
D) 
E) 
and find the particular solution that passes through the points , A)
B)
C)
D)
E)
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Deck 11: Differential Equations
1
Determine whether the function is a solution of the differential equation
A) Solution
B) Not a solution
is a solution of the differential equation A) Solution
B) Not a solution
Not a solution
2
Determine whether the function is a solution of the differential equation
A) Not a solution
B) Solution
is a solution of the differential equation A) Not a solution
B) Solution
Not a solution
3
Which of the following is a solution of the differential equation ?
A)
B)
C)
D)
E)
? A)
B)
C)
D)
E)
4
Use the integration to find the general solution of the differential equation
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Determine whether is a solution of the differential equation
A) and
B) and
C) and
D) and
E) and
is a solution of the differential equation A)
and B)
and C)
and D)
and E)
and Unlock Deck
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6
Determine whether is a solution of the differential equation
A)
B)
C)
D)
E)
is a solution of the differential equation A)
B)
C)
D)
E)
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7
Verify that the general solution satisfies the differential equation.Then find the particular solution that satisfies the initial condition.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Determine whether is a solution of the differential equation
A) and
B) and
C) and
D) and
E) and
is a solution of the differential equation A)
and B)
and C)
and D)
and E)
and Unlock Deck
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9
Use the integration to find the general solution of the differential equation
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Use integration to find a general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Which of the following is a solution of the differential equation ?
A)
B)
C)
D)
E)
? A)
B)
C)
D)
E)
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12
Use the integration to find the general solution of the differential equation
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Determine whether the function is a solution of the differential equation
A) Solution
B) Not a solution
is a solution of the differential equation A) Solution
B) Not a solution
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14
Determine whether the function is a solution of the differential equation
A) Not a solution
B) Solution
is a solution of the differential equation A) Not a solution
B) Solution
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15
Some of the curves corresponding to different values of C in general solution of the differential equation , are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph.
A)
B)
C)
D)
E)
, are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph. A)
B)
C)
D)
E)
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16
Verify that the general solution satisfies the differential equation.Then find the particular solution that satisfies the initial condition.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Some of the curves corresponding to different values of C in general solution of the differential equation , are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph.
A)
B)
C)
D)
E)
, are shown in the figure given below.Find the particular solution that passes through the points plotted on the graph.
A)
B)
C)
D)
E)
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18
Determine whether is a solution of the differential equation
A) and
B) and
C) and
D) and
E) and
is a solution of the differential equation A)
and B)
and C)
and D)
and E)
and Unlock Deck
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19
Use integration to find a general solution of the differential equation
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution.
A)
B)
C)
D)
E)
that satisfies the initial condition when ,where is the general solution. A)
B)
C)
D)
E)
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21
The isotope has a half-life of 1,599 years.Given an initial amount of 13 grams of the isotope,how many grams will remain after 1,500 years? After 15,000 years? Round your answers to four decimal places.
A) 4.7495 g, 0.0137 g
B) 2.714 g, 0.0078 g
C) 6.785 g, 0.0195 g
D) 8.142 g, 0.0234 g
E) 4.071 g,0.0273 g
has a half-life of 1,599 years.Given an initial amount of 13 grams of the isotope,how many grams will remain after 1,500 years? After 15,000 years? Round your answers to four decimal places. A) 4.7495 g, 0.0137 g
B) 2.714 g, 0.0078 g
C) 6.785 g, 0.0195 g
D) 8.142 g, 0.0234 g
E) 4.071 g,0.0273 g
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22
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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23
Write the the differential equation by separating the variables.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
Use the initial condition to find the particular solution of the differential equation. , when
A)
B)
C)
D)
E)
, when A)
B)
C)
D)
E)
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26
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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27
Use the initial condition to find the particular solution of the differential equation. , when
A)
B)
C)
D)
E)
, when A)
B)
C)
D)
E)
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28
Use the initial condition to find the particular solution of the differential equation. , when
A)
B)
C)
D)
E)
, when A)
B)
C)
D)
E)
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29
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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31
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
Write the the differential equation by separating the variables.
A)
B)
C)
D) No, the variables cannot be separated
E)
A)
B)
C)
D) No, the variables cannot be separated
E)
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33
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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34
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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35
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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36
Solve the differential equation to find velocity v as a function of time t if when The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity,friction,and air resistance.
A)
B)
C)
D)
E)
when The differential equation models the motion of two people on a toboggan after consideration of the forces of gravity,friction,and air resistance. A)
B)
C)
D)
E)
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37
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Find an equation of the graph that passes through the point and has the specified slope.Then graph the equation.
Point: ,
Slope:
A)
B)
C)
D)
E) None of the above
Point:
,Slope:
A)
B)
C)
D)
E) None of the above
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39
Use the initial condition to find the particular solution of the differential equation. , when
A)
B)
C)
D)
E)
, when A)
B)
C)
D)
E)
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40
Write the the differential equation by separating the variables.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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41
Write the first-order linear differential equation in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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42
Solve for y in two ways.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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43
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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44
Find the particular solution that satisfies the initial condition. ; Initial Condition: when
A)
B)
C)
D)
E)
; Initial Condition: when A)
B)
C)
D)
E)
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45
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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46
Find the particular solution of the differential equation passing through the point
A)
B)
C)
D)
E)
passing through the point A)
B)
C)
D)
E)
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47
Write the first-order linear differential equation in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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49
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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51
Find the solution of the differential equation ,without solving it.
A)
B)
C)
D)
E)
,without solving it. A)
B)
C)
D)
E)
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52
Write the first-order linear differential equation in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Find the particular solution that satisfies the initial condition. ; Initial Condition: when
A)
B)
C)
D)
E)
; Initial Condition: when A)
B)
C)
D)
E)
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54
Solve for y in two ways.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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55
A calf that weighs 75 pounds at birth gains weight at the rate ,where w is weight in pounds and t is time in years.Use a computer algebra system to solve the differential equation for
A)
B)
C)
D)
E)
,where w is weight in pounds and t is time in years.Use a computer algebra system to solve the differential equation for A)
B)
C)
D)
E)
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56
Find the particular solution that satisfies the initial condition. ; Initial Condition: when
A)
B)
C)
D)
E)
; Initial Condition: when A)
B)
C)
D)
E)
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57
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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58
Find the particular solution of the differential equation that satisfies the boundary condition
A)
B)
C)
D)
E)
that satisfies the boundary condition A)
B)
C)
D)
E)
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59
Find the solution of the differential equation ,without solving it.
A)
B)
C)
D)
E)
,without solving it. A)
B)
C)
D)
E)
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60
Find the particular solution that satisfies the initial condition. ; Initial Condition: when
A)
B)
C)
D)
E)
; Initial Condition: when A)
B)
C)
D)
E)
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61
The rate of change in sales S (in thousands of units)of a new product is proportional to the difference between L and S at any time t (in years),where L is the maximum number of units of the new product available.When , Write and solve the differential equation for this sales model.
A)
B)
C)
D)
E)
, Write and solve the differential equation for this sales model. A)
B)
C)
D)
E)
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62
Use this equation and find P if the corporation needs $120,000,000 in 8 years and the fund earns 8% interest compounded continuously.
A) $110,708,538.49
B) $10,500,538.49
C) $10,708,538.49
D) $100,708,538.49
E) $1,708,538.49
and find P if the corporation needs $120,000,000 in 8 years and the fund earns 8% interest compounded continuously. A) $110,708,538.49
B) $10,500,538.49
C) $10,708,538.49
D) $100,708,538.49
E) $1,708,538.49
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63
The rate of change of the population of a city is proportional to the population P at any time (in years).In 2000,the population was 200,000,and the constant of proportionality was 0.015.Estimate the population of the city in the year 2020.
A) 260,972 people
B) 268,972 people
C) 263,972 people
D) 266,972 people
E) 269,972 people
A) 260,972 people
B) 268,972 people
C) 263,972 people
D) 266,972 people
E) 269,972 people
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64
A 200-gallon tank is full of a solution containing 55 pounds of concentrate.Starting at time t=0 ,distilled water is added to the tank at a rate of 20 gallons per minute,and the well-stirred solution is withdrawn at the same rate.Find the amount of concentrate Q in the solution as a function of t.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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65
A large corporation starts at time to invest part of its profit at a rate of P dollars per year in a fund for future expansion.Assume that the fund earns r percent interest per year compounded continuously.The rate of growth of the amount A in the fund is given by where when and r is in decimal form.Solve this differential equation for A as a function of t.
A)
B)
C)
D)
E)
to invest part of its profit at a rate of P dollars per year in a fund for future expansion.Assume that the fund earns r percent interest per year compounded continuously.The rate of growth of the amount A in the fund is given by where when and r is in decimal form.Solve this differential equation for A as a function of t. A)
B)
C)
D)
E)
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66
A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate proportional to its moisture content.After 1 hour,the towel has lost 40% of its original moisture content.How long will it take the towel to lose 80% of its original moisture content?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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67
Assume that the rate of change in y is proportional to y.Solve the resulting differential equation and find the particular solution that passes through the points ,
A)
B)
C)
D)
E)
and find the particular solution that passes through the points , A)
B)
C)
D)
E)
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68
During a chemical reaction,a compound changes into another compound at a rate proportional to the unchanged amount y.Write the differential equation for the chemical reaction model.Find the particular solution when the initial amount of the original compound is 20 grams and the amount remaining after 1 hour is 16 grams.
A) ,
B) ,
C) ,
D) ,
E) ,
A)
, B)
, C)
, D)
, E)
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69
Use the chemical reaction model described to find the amount y (in grams)as a function of time t (in hours).Then use a graphing utility to graph the function. grams when ; grams when
A)
B)
C)
D)
E)
grams when ; grams when A)
B)
C)
D)
E)
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70
Use the Gompertz growth model described to find the population y as a function of time t (in years). when ; when
A)
B)
C)
D)
E)
when ; when A)
B)
C)
D)
E)
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71
A medical researcher wants to determine the concentration C (in moles per liter)of a tracer drug injected into a moving fluid with flow R (in liters per minute).Solve this problem by considering a single-compartment dilution model (see figure).Assume that the fluid is continuously mixed and that the volume V (in liters)of fluid in the compartment is constant.
If the tracer is injected instantaneously at time ,then the concentration of the fluid in the compartment begins diluting according to the differential equation , when (a)Solve this differential equation to find the concentration as a function of time.
(b)Find the limit of C as
A) a.
b) 1
B) a.
b) 0
C) a.
b) 2
D) a.
b) 0
E) a.
b)1
If the tracer is injected instantaneously at time
,then the concentration of the fluid in the compartment begins diluting according to the differential equation , when (a)Solve this differential equation to find the concentration as a function of time.(b)Find the limit of C as
A) a.
b) 1
B) a.
b) 0
C) a.
b) 2
D) a.
b) 0
E) a.
b)1
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72
A population of eight beavers has been introduced into a new wetlands area.Biologists estimate that the maximum population the wetlands can sustain is 60 beavers.After 3 years,the population is 15 beavers.The population follows a Gompertz growth model.How many beavers will there be in the wetlands after 10 years?
A) 34 beavers
B) 32 beavers
C) 30 beavers
D) 31 beavers
E) 39 beavers
A) 34 beavers
B) 32 beavers
C) 30 beavers
D) 31 beavers
E) 39 beavers
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73
Assume that the rate of change in is proportional to Solve the resulting differential equation and find the particular solution that passes through the points ,
A)
B)
C)
D)
E)
is proportional to Solve the resulting differential equation and find the particular solution that passes through the points , A)
B)
C)
D)
E)
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74
Use this equation and find A for each situation.
(a) , and years
(b) , and years
A) a) 685,099.00
b) 5,802,815.12
B) a) 585,099.00
b) 5,802,815.12
C) a) 685,099.00
b) 6,802,815.12
D) a) 585,099.00
b) 4,802,815.12
E)
a)485,099.00
b)5,802,815.12
and find A for each situation. (a)
, and years(b)
, and years
A) a) 685,099.00
b) 5,802,815.12
B) a) 585,099.00
b) 5,802,815.12
C) a) 685,099.00
b) 6,802,815.12
D) a) 585,099.00
b) 4,802,815.12
E)
a)485,099.00
b)5,802,815.12
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75
Use the hybrid selection model described to find the percent y (in decimal form)of the population that has the indicated characteristics as a function of time t (in generations). when ; when
A)
B)
C)
D)
E)
when ; when A)
B)
C)
D)
E)
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76
Use the advertising awareness model described to find the number of people y (in millions)aware of the product as a function of time t (in years). when ; when
A)
B)
C)
D)
E)
when ; when A)
B)
C)
D)
E)
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77
Assume that the rate of change in y is proportional to y.Solve the resulting differential equation and find the particular solution that passes through the points ,
A)
B)
C)
D)
E)
and find the particular solution that passes through the points , A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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