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Find the particular solution of the differential equation Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    ​ B)    C)    D)    E)   that satisfies the boundary condition Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    ​ B)    C)    D)    E)   . ​


A) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    ​ B)    C)    D)    E)
B) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    ​ B)    C)    D)    E)
C) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    ​ B)    C)    D)    E)
D) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    ​ B)    C)    D)    E)
E) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    ​ B)    C)    D)    E)

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Find the time (in years) necessary for 1,000 to double if it is invested at a rate 6% compounded continuously. Round your answer to two decimal places. ​


A) 1.16 years
B) 11.55 years
C) 1.39 years
D) 11.90 years
E) 11.58 years

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We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​ We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​   , ​   . ​ Find the population equilibrium point. ​ A)    B)    C)    D)    E)   , ​ We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​   , ​   . ​ Find the population equilibrium point. ​ A)    B)    C)    D)    E)   . ​ Find the population equilibrium point. ​


A) We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​   , ​   . ​ Find the population equilibrium point. ​ A)    B)    C)    D)    E)
B) We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​   , ​   . ​ Find the population equilibrium point. ​ A)    B)    C)    D)    E)
C) We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​   , ​   . ​ Find the population equilibrium point. ​ A)    B)    C)    D)    E)
D) We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​   , ​   . ​ Find the population equilibrium point. ​ A)    B)    C)    D)    E)
E) We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​   , ​   . ​ Find the population equilibrium point. ​ A)    B)    C)    D)    E)

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A calf that weighs 75 pounds at birth gains weight at the rate 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. If the animal is sold when its weight reaches 900 pounds, find the time of sale using the model   . Round your answer to two decimal places. ​ A)  7.02 years B)  2.76 years C)  1.12 years D)  1.08 years E)  0.44 year where w is weight in pounds and t is time in years. If the animal is sold when its weight reaches 900 pounds, find the time of sale using the model 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. If the animal is sold when its weight reaches 900 pounds, find the time of sale using the model   . Round your answer to two decimal places. ​ A)  7.02 years B)  2.76 years C)  1.12 years D)  1.08 years E)  0.44 year . Round your answer to two decimal places. ​


A) 7.02 years
B) 2.76 years
C) 1.12 years
D) 1.08 years
E) 0.44 year

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Select from the choices below the slope field for the differential equation. ​ Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above


A) Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above
B) Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above
C) Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above
D) Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above
E) none of the above

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


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

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Find the logistic equation that satisfies the following differential equation and initial condition. ​ Find the logistic equation that satisfies the following differential equation and initial condition. ​   ,   ​ A)    B)    C)    D)    E)  none of these , Find the logistic equation that satisfies the following differential equation and initial condition. ​   ,   ​ A)    B)    C)    D)    E)  none of these


A) Find the logistic equation that satisfies the following differential equation and initial condition. ​   ,   ​ A)    B)    C)    D)    E)  none of these
B) Find the logistic equation that satisfies the following differential equation and initial condition. ​   ,   ​ A)    B)    C)    D)    E)  none of these
C) Find the logistic equation that satisfies the following differential equation and initial condition. ​   ,   ​ A)    B)    C)    D)    E)  none of these
D) Find the logistic equation that satisfies the following differential equation and initial condition. ​   ,   ​ A)    B)    C)    D)    E)  none of these
E) none of these

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Suppose an eight-pound object is dropped from a height of 5,000 feet, where the air resistance is proportional to the velocity. Write the velocity as a function of time if its velocity after 4 seconds is approximately -50 feet per second. Use a graphing utility or a computer algebra system. Round numerical answers in your answer to four places. ​


A) Suppose an eight-pound object is dropped from a height of 5,000 feet, where the air resistance is proportional to the velocity. Write the velocity as a function of time if its velocity after 4 seconds is approximately -50 feet per second. Use a graphing utility or a computer algebra system. Round numerical answers in your answer to four places. ​ A)    B)    C)    D)    E)
B) Suppose an eight-pound object is dropped from a height of 5,000 feet, where the air resistance is proportional to the velocity. Write the velocity as a function of time if its velocity after 4 seconds is approximately -50 feet per second. Use a graphing utility or a computer algebra system. Round numerical answers in your answer to four places. ​ A)    B)    C)    D)    E)
C) Suppose an eight-pound object is dropped from a height of 5,000 feet, where the air resistance is proportional to the velocity. Write the velocity as a function of time if its velocity after 4 seconds is approximately -50 feet per second. Use a graphing utility or a computer algebra system. Round numerical answers in your answer to four places. ​ A)    B)    C)    D)    E)
D) Suppose an eight-pound object is dropped from a height of 5,000 feet, where the air resistance is proportional to the velocity. Write the velocity as a function of time if its velocity after 4 seconds is approximately -50 feet per second. Use a graphing utility or a computer algebra system. Round numerical answers in your answer to four places. ​ A)    B)    C)    D)    E)
E) Suppose an eight-pound object is dropped from a height of 5,000 feet, where the air resistance is proportional to the velocity. Write the velocity as a function of time if its velocity after 4 seconds is approximately -50 feet per second. Use a graphing utility or a computer algebra system. Round numerical answers in your answer to four places. ​ A)    B)    C)    D)    E)

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The initial investment in a savings account in which interest is compounded continuously is $768. If the time required to double the amount is The initial investment in a savings account in which interest is compounded continuously is $768. If the time required to double the amount is   years, what is the amount after 13 years? Round your answer to the nearest cent. ​ A)  $2,090.17 B)  $1,982.88 C)  $2,101.89 D)  $1,582.88 E)  $10,525.90 years, what is the amount after 13 years? Round your answer to the nearest cent. ​


A) $2,090.17
B) $1,982.88
C) $2,101.89
D) $1,582.88
E) $10,525.90

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


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

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Which of the following is a solution of the differential equation Which of the following is a solution of the differential equation   ? ​ A)    B)    C)    D)    E)   ? ​


A) Which of the following is a solution of the differential equation   ? ​ A)    B)    C)    D)    E)
B) Which of the following is a solution of the differential equation   ? ​ A)    B)    C)    D)    E)
C) Which of the following is a solution of the differential equation   ? ​ A)    B)    C)    D)    E)
D) Which of the following is a solution of the differential equation   ? ​ A)    B)    C)    D)    E)
E) Which of the following is a solution of the differential equation   ? ​ A)    B)    C)    D)    E)

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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)

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A calf that weighs 50 pounds at birth gains weight at the rate A calf that weighs 50 pounds at birth gains weight at the rate   where w is weight in pounds and t is time in years. What is the maximum weight of the animal if one uses the model   ? ​ A)  1200 lb B)  750 lb C)  1150 lb D)  1250 lb E)  1900 lb where w is weight in pounds and t is time in years. What is the maximum weight of the animal if one uses the model A calf that weighs 50 pounds at birth gains weight at the rate   where w is weight in pounds and t is time in years. What is the maximum weight of the animal if one uses the model   ? ​ A)  1200 lb B)  750 lb C)  1150 lb D)  1250 lb E)  1900 lb ? ​


A) 1200 lb
B) 750 lb
C) 1150 lb
D) 1250 lb
E) 1900 lb

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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)

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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)

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A 200-gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time A 200-gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time   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 time at which the amount of concentrate in the tank reaches 15 pounds. Round your answer to one decimal place. A)  2.2 min B)  1.8 min C)  10.2 min D)  5.1 min E)  10.2 min. 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 time at which the amount of concentrate in the tank reaches 15 pounds. Round your answer to one decimal place.


A) 2.2 min
B) 1.8 min
C) 10.2 min
D) 5.1 min
E) 10.2 min.

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Find the particular solution of the differential equation Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    B)    C)    D)    E)   that satisfies the boundary condition Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    B)    C)    D)    E)   . ​


A) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    B)    C)    D)    E)
B) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    B)    C)    D)    E)
C) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    B)    C)    D)    E)
D) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    B)    C)    D)    E)
E) Find the particular solution of the differential equation   that satisfies the boundary condition   . ​ A)    B)    C)    D)    E)

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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 satisfying the condition   . ​ A)    B)    C)    D)    E)   and use the slope field to sketch the solution satisfying the condition Sketch the slope field for the differential equation   and use the slope field to sketch the solution satisfying the condition   . ​ A)    B)    C)    D)    E)   . ​


A) Sketch the slope field for the differential equation   and use the slope field to sketch the solution satisfying the condition   . ​ A)    B)    C)    D)    E)
B) Sketch the slope field for the differential equation   and use the slope field to sketch the solution satisfying the condition   . ​ A)    B)    C)    D)    E)
C) Sketch the slope field for the differential equation   and use the slope field to sketch the solution satisfying the condition   . ​ A)    B)    C)    D)    E)
D) Sketch the slope field for the differential equation   and use the slope field to sketch the solution satisfying the condition   . ​ A)    B)    C)    D)    E)
E) Sketch the slope field for the differential equation   and use the slope field to sketch the solution satisfying the condition   . ​ A)    B)    C)    D)    E)

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Select from the choices below the slope field for the differential equation. ​ Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above


A) Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above
B) Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above
C) Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above
D) Select from the choices below the slope field for the differential equation. ​   ​ A)    B)    C)    D)    E)  none of the above
E) none of the above

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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)

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