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​Consider the differential equation ​ ​Consider the differential equation ​ ,for ​ only,with initial value . ​ Which of the following is the slope field for the general solution to the given differential equation?​ ​ A) ​ B) ​ C) ​ D) ​ ,for ​ ​Consider the differential equation ​ ,for ​ only,with initial value . ​ Which of the following is the slope field for the general solution to the given differential equation?​ ​ A) ​ B) ​ C) ​ D) ​ only,with initial value ​Consider the differential equation ​ ,for ​ only,with initial value . ​ Which of the following is the slope field for the general solution to the given differential equation?​ ​ A) ​ B) ​ C) ​ D) ​ . ​ Which of the following is the slope field for the general solution to the given differential equation?​ ​


A) ​
​Consider the differential equation ​ ,for ​ only,with initial value . ​ Which of the following is the slope field for the general solution to the given differential equation?​ ​ A) ​ B) ​ C) ​ D) ​
B) ​
​Consider the differential equation ​ ,for ​ only,with initial value . ​ Which of the following is the slope field for the general solution to the given differential equation?​ ​ A) ​ B) ​ C) ​ D) ​
C) ​
​Consider the differential equation ​ ,for ​ only,with initial value . ​ Which of the following is the slope field for the general solution to the given differential equation?​ ​ A) ​ B) ​ C) ​ D) ​
D) ​
​Consider the differential equation ​ ,for ​ only,with initial value . ​ Which of the following is the slope field for the general solution to the given differential equation?​ ​ A) ​ B) ​ C) ​ D) ​

E) A) and B)
F) All of the above

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Solve the differential equation Solve the differential equation . ​ A) B) C) D) E) . ​


A) Solve the differential equation . ​ A) B) C) D) E)
B) Solve the differential equation . ​ A) B) C) D) E)
C) Solve the differential equation . ​ A) B) C) D) E)
D) Solve the differential equation . ​ A) B) C) D) E)
E) Solve the differential equation . ​ A) B) C) D) E)

F) A) and B)
G) All of the above

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The logistic function The logistic function models the growth of a population.Identify the value of k. ​ A) 3.5 B) 4 C) 2 D) 10 E) 3 models the growth of a population.Identify the value of k. ​


A) 3.5
B) 4
C) 2
D) 10
E) 3

F) A) and B)
G) C) and D)

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​Consider the differential equation ​Consider the differential equation ,for which the solution is g(x) .​ ​Let y(x) be the particular solution that contains (0,1) .Using Euler's Method with step size ,what is the estimate for ? ​ A) ​4 B) ​3.5 C) ​3 D) ​4.5 ,for which the solution is g(x) .​ ​Let y(x) be the particular solution that contains (0,1) .Using Euler's Method with step size ​Consider the differential equation ,for which the solution is g(x) .​ ​Let y(x) be the particular solution that contains (0,1) .Using Euler's Method with step size ,what is the estimate for ? ​ A) ​4 B) ​3.5 C) ​3 D) ​4.5 ,what is the estimate for ​Consider the differential equation ,for which the solution is g(x) .​ ​Let y(x) be the particular solution that contains (0,1) .Using Euler's Method with step size ,what is the estimate for ? ​ A) ​4 B) ​3.5 C) ​3 D) ​4.5 ? ​


A) ​4
B) ​3.5
C) ​3
D) ​4.5

E) A) and D)
F) None of the above

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Use integration to find a general solution of the differential equation. ​ Use integration to find a general solution of the differential equation. ​ ​ A) B) C) D) E) ​


A) Use integration to find a general solution of the differential equation. ​ ​ A) B) C) D) E)
B) Use integration to find a general solution of the differential equation. ​ ​ A) B) C) D) E)
C) Use integration to find a general solution of the differential equation. ​ ​ A) B) C) D) E)
D) Use integration to find a general solution of the differential equation. ​ ​ A) B) C) D) E)
E) Use integration to find a general solution of the differential equation. ​ ​ A) B) C) D) E)

F) B) and E)
G) B) and D)

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Find the particular solution of the differential equation 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 Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​ A) B) C) D) E) when Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​ A) B) C) D) E) ,where Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​ A) B) C) D) E) is the general solution. ​


A) Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​ A) B) C) D) E)
B) Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​ A) B) C) D) E)
C) Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​ A) B) C) D) E)
D) Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​ A) B) C) D) E)
E) Find the particular solution of the differential equation that satisfies the initial condition when ,where is the general solution. ​ A) B) C) D) E)

F) A) and B)
G) C) and D)

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A calf that weighs 60 pounds at birth gains weight at the rate A calf that weighs 60 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years.If the animal is sold when its weight reaches 650 pounds,find the time of sale using the model .Round your answer to two decimal places. ​ A) 7.31 years B) 2.65 years C) 1.07 years D) 0.72 year E) 0.29 year where w is weight in pounds and t is time in years.If the animal is sold when its weight reaches 650 pounds,find the time of sale using the model A calf that weighs 60 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years.If the animal is sold when its weight reaches 650 pounds,find the time of sale using the model .Round your answer to two decimal places. ​ A) 7.31 years B) 2.65 years C) 1.07 years D) 0.72 year E) 0.29 year .Round your answer to two decimal places. ​


A) 7.31 years
B) 2.65 years
C) 1.07 years
D) 0.72 year
E) 0.29 year

F) All of the above
G) C) and D)

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Solve the differential equation in Solve the differential equation in to find f(x)in terms of x only.​ to find f(x)in terms of x only.​

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Rewrite blured image ​
Separatin...

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Sketch the slope field for the differential equation Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point . ​ A) ​ B) ​ C) ​ D) ​ E) ​ and use the slope field to sketch the solution that passes through the point Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point . ​ A) ​ B) ​ C) ​ D) ​ E) ​ . ​


A) ​
Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point . ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​
Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point . ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​
Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point . ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​
Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point . ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​
Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point . ​ A) ​ B) ​ C) ​ D) ​ E) ​

F) A) and E)
G) All of the above

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The half-life of the carbon isotope C-14 is approximately 5,715 years.If the amount left after 3,000 years is 1.8 g,what is the amount after 6,000 years? Round your answer to three decimal places. ​


A) 1.251 g
B) 1.043 g
C) 1.800 g
D) 0.604 g
E) 2.502 g

F) B) and D)
G) A) and B)

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A

Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E) ​ Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E) ​


A) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
B) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
C) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
D) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
E) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)

F) A) and B)
G) B) and E)

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A container of hot liquid is placed in a freezer that is kept at a constant temperature of A container of hot liquid is placed in a freezer that is kept at a constant temperature of .The initial temperature of the liquid is .After 5 minutes,the liquid's temperature is .How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places. ​ A) 5.29 minutes B) 7.94 minutes C) 8.82 minutes D) 3.53 minutes E) 9.70 minutes .The initial temperature of the liquid is A container of hot liquid is placed in a freezer that is kept at a constant temperature of .The initial temperature of the liquid is .After 5 minutes,the liquid's temperature is .How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places. ​ A) 5.29 minutes B) 7.94 minutes C) 8.82 minutes D) 3.53 minutes E) 9.70 minutes .After 5 minutes,the liquid's temperature is A container of hot liquid is placed in a freezer that is kept at a constant temperature of .The initial temperature of the liquid is .After 5 minutes,the liquid's temperature is .How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places. ​ A) 5.29 minutes B) 7.94 minutes C) 8.82 minutes D) 3.53 minutes E) 9.70 minutes .How much longer will it take for its temperature to decrease to A container of hot liquid is placed in a freezer that is kept at a constant temperature of .The initial temperature of the liquid is .After 5 minutes,the liquid's temperature is .How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places. ​ A) 5.29 minutes B) 7.94 minutes C) 8.82 minutes D) 3.53 minutes E) 9.70 minutes ? Round your answer to two decimal places. ​


A) 5.29 minutes
B) 7.94 minutes
C) 8.82 minutes
D) 3.53 minutes
E) 9.70 minutes

F) All of the above
G) A) and E)

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The logistic function The logistic function models the growth of a population.Determine when the population reaches one-half of the maximum carrying capacity.Round your answer to three decimal places. ​ A) 0.549 B) 3.333 C) 1.151 D) 5.000 E) 1.000 models the growth of a population.Determine when the population reaches one-half of the maximum carrying capacity.Round your answer to three decimal places. ​


A) 0.549
B) 3.333
C) 1.151
D) 5.000
E) 1.000

F) B) and E)
G) A) and C)

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A

Each of the following graphs is from a logistic function Each of the following graphs is from a logistic function .Which one has the smallest value of b? ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​ .Which one has the smallest value of b? ​


A) ​
Each of the following graphs is from a logistic function .Which one has the smallest value of b? ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​
​
B) ​
Each of the following graphs is from a logistic function .Which one has the smallest value of b? ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​
C) ​
Each of the following graphs is from a logistic function .Which one has the smallest value of b? ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​
D) ​
Each of the following graphs is from a logistic function .Which one has the smallest value of b? ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​
E) ​
Each of the following graphs is from a logistic function .Which one has the smallest value of b? ​ A) ​ ​ B) ​ C) ​ D) ​ E) ​

F) C) and E)
G) A) and E)

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E

Find the function Find the function passing through the point with the first derivative . ​ A) B) C) D) E) passing through the point Find the function passing through the point with the first derivative . ​ A) B) C) D) E) with the first derivative Find the function passing through the point with the first derivative . ​ A) B) C) D) E) . ​


A) Find the function passing through the point with the first derivative . ​ A) B) C) D) E)
B) Find the function passing through the point with the first derivative . ​ A) B) C) D) E)
C) Find the function passing through the point with the first derivative . ​ A) B) C) D) E)
D) Find the function passing through the point with the first derivative . ​ A) B) C) D) E)
E) Find the function passing through the point with the first derivative . ​ A) B) C) D) E)

F) C) and E)
G) A) and C)

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Find the orthogonal trajectories of the family ​ Find the orthogonal trajectories of the family ​ . ​ A) B) C) D) E) . ​


A) Find the orthogonal trajectories of the family ​ . ​ A) B) C) D) E)
B) Find the orthogonal trajectories of the family ​ . ​ A) B) C) D) E)
C) Find the orthogonal trajectories of the family ​ . ​ A) B) C) D) E)
D) Find the orthogonal trajectories of the family ​ . ​ A) B) C) D) E)
E) Find the orthogonal trajectories of the family ​ . ​ A) B) C) D) E)

F) None of the above
G) A) and B)

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Use the differential equation Use the differential equation and its slope field to find the slope at the point . ​ ​ A) -32 B) -1 C) -8 D) -64 E) 16 and its slope field to find the slope at the point Use the differential equation and its slope field to find the slope at the point . ​ ​ A) -32 B) -1 C) -8 D) -64 E) 16 . ​ Use the differential equation and its slope field to find the slope at the point . ​ ​ A) -32 B) -1 C) -8 D) -64 E) 16 ​


A) -32
B) -1
C) -8
D) -64
E) 16

F) A) and C)
G) None of the above

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Find the orthogonal trajectories of the family Find the orthogonal trajectories of the family . ​ A) B) C) D) E) . ​


A) Find the orthogonal trajectories of the family . ​ A) B) C) D) E)
B) Find the orthogonal trajectories of the family . ​ A) B) C) D) E)
C) Find the orthogonal trajectories of the family . ​ A) B) C) D) E)
D) Find the orthogonal trajectories of the family . ​ A) B) C) D) E)
E) Find the orthogonal trajectories of the family . ​ A) B) C) D) E)

F) B) and E)
G) A) and B)

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Consider the differential equation Consider the differential equation ​,for which the solution is .Let . The particular solution is ​ A) ​ B) ​ C) ​ D) ​ ​,for which the solution is Consider the differential equation ​,for which the solution is .Let . The particular solution is ​ A) ​ B) ​ C) ​ D) ​ .Let Consider the differential equation ​,for which the solution is .Let . The particular solution is ​ A) ​ B) ​ C) ​ D) ​ . The particular solution is ​


A) ​ Consider the differential equation ​,for which the solution is .Let . The particular solution is ​ A) ​ B) ​ C) ​ D) ​
B) ​ Consider the differential equation ​,for which the solution is .Let . The particular solution is ​ A) ​ B) ​ C) ​ D) ​
C) ​ Consider the differential equation ​,for which the solution is .Let . The particular solution is ​ A) ​ B) ​ C) ​ D) ​
D) ​ Consider the differential equation ​,for which the solution is .Let . The particular solution is ​ A) ​ B) ​ C) ​ D) ​

E) B) and C)
F) None of the above

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Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E) ​


A) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)
B) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)
C) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)
D) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)
E) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)

F) A) and B)
G) B) and D)

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