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Exam 9: Differential Equations

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Exam 1: Functions and Models160 Questionsadd course
Exam 2: Limits and Derivatives160 Questionsadd course
Exam 3: Differentiation Rules160 Questionsadd course
Exam 4: Applications of Differentiation159 Questionsadd course
Exam 5: Integrals160 Questionsadd course
Exam 6: Applications of Integration160 Questionsadd course
Exam 7: Techniques of Integration160 Questionsadd course
Exam 8: Further Applications of Integration160 Questionsadd course
Exam 9: Differential Equations160 Questionsadd course
Exam 10: Parametric Equations and Polar Coordinates160 Questionsadd course
Exam 11: Infinite Sequences and Series160 Questionsadd course
Exam 12: Vectors and the Geometry of Space159 Questionsadd course
Exam 13: Vector Functions160 Questionsadd course
Exam 14: Partial Derivatives158 Questionsadd course
Exam 15: Multiple Integrals160 Questionsadd course
Exam 16: Vector Calculus160 Questionsadd course
Exam 17: Second-Order Differential Equations160 Questionsadd course
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Biologists stocked a lake with Biologists stocked a lake with fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be The number of fish tripled in the first year.Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be Biologists stocked a lake with fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be The number of fish tripled in the first year.Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after The number of fish tripled in the first year.Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after Biologists stocked a lake with fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be The number of fish tripled in the first year.Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after

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Question 41

Suppose that a population grows according to a logistic model with carrying capacity Suppose that a population grows according to a logistic model with carrying capacity and per year.Write the logistic differential equation for these data. and Suppose that a population grows according to a logistic model with carrying capacity and per year.Write the logistic differential equation for these data. per year.Write the logistic differential equation for these data.

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Question 42

Let c be a positive number.A differential equation of the form Let c be a positive number.A differential equation of the form where is a positive constant, is called because the exponent in the expression is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday? where Let c be a positive number.A differential equation of the form where is a positive constant, is called because the exponent in the expression is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday? is a positive constant, is called Let c be a positive number.A differential equation of the form where is a positive constant, is called because the exponent in the expression is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday? because the exponent in the expression Let c be a positive number.A differential equation of the form where is a positive constant, is called because the exponent in the expression is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday? is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term Let c be a positive number.A differential equation of the form where is a positive constant, is called because the exponent in the expression is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday? If Let c be a positive number.A differential equation of the form where is a positive constant, is called because the exponent in the expression is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday? such rabbits breed initially and the warren has Let c be a positive number.A differential equation of the form where is a positive constant, is called because the exponent in the expression is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday? rabbits after months, then when is doomsday? Let c be a positive number.A differential equation of the form where is a positive constant, is called because the exponent in the expression is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday?

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Question 43

Solve the differential equation.Select the correct Answer Solve the differential equation.Select the correct Answer

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Question 44

Select the correct Answer: for each question. -Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached Select the correct Answer: for each question. -Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? and is placed on a table in a room where the temperature is Select the correct Answer: for each question. -Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? If Select the correct Answer: for each question. -Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? is the temperature of the turkey after Select the correct Answer: for each question. -Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? minutes, then Newton's Law of Cooling implies that Select the correct Answer: for each question. -Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? This could be solved as a separable differential equation.Another method is to make the change of variable Select the correct Answer: for each question. -Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? If the temperature of the turkey is Select the correct Answer: for each question. -Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? after half an hour, what is the temperature after 35 min?

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Question 45

Consider a population Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition with constant relative birth and death rates Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition and Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition respectively, and a constant emigration rate Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition , where Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition and Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition Then the rate of change of the population at time Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition is modeled by the differential equation Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition where Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition Find the solution of this equation with the rate of change of the population at time Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition that satisfies the initial condition Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition

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Question 46

Which equation does the function Which equation does the function satisfy? Select the correct Answer satisfy? Select the correct Answer

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Question 47

A phase trajectory is shown for populations of rabbits A phase trajectory is shown for populations of rabbits and foxes Describe how each population changes as time goes by. Select the correct statement. and foxes A phase trajectory is shown for populations of rabbits and foxes Describe how each population changes as time goes by. Select the correct statement. Describe how each population changes as time goes by. A phase trajectory is shown for populations of rabbits and foxes Describe how each population changes as time goes by. Select the correct statement. Select the correct statement.

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Question 48

Select the correct Answer: for each question. -Solve the differential equation. Select the correct Answer: for each question. -Solve the differential equation.

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Question 49

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? and is placed on a table in a room where the temperature is Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? If Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? is the temperature of the turkey after Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? minutes, then Newton's Law of Cooling implies that Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? This could be solved as a separable differential equation.Another method is to make the change of variable Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? If the temperature of the turkey is Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is If is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? after half an hour, what is the temperature after 35 min?

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Question 50

Solve the differential equation. Solve the differential equation.

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Question 51

Find the orthogonal trajectories of the family of curves. Find the orthogonal trajectories of the family of curves.

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Question 52

Choose the differential equation corresponding to this direction field. Choose the differential equation corresponding to this direction field.

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Question 53

Select the correct Answer: for each question. -Suppose that a population grows according to a logistic model with carrying capacity Select the correct Answer: for each question. -Suppose that a population grows according to a logistic model with carrying capacity and per year.Choose the logistic differential equation for these data. and Select the correct Answer: for each question. -Suppose that a population grows according to a logistic model with carrying capacity and per year.Choose the logistic differential equation for these data. per year.Choose the logistic differential equation for these data.

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Question 54

Solve the initial-value problem. Solve the initial-value problem.

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Question 55

Let c be a positive number.A differential equation of the form Let c be a positive number.A differential equation of the form where is a positive constant is called a because the exponent in the expression is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term such rabbits breed initially and the warren has rabbits after months, then when is doomsday? where Let c be a positive number.A differential equation of the form where is a positive constant is called a because the exponent in the expression is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term such rabbits breed initially and the warren has rabbits after months, then when is doomsday? is a positive constant is called a Let c be a positive number.A differential equation of the form where is a positive constant is called a because the exponent in the expression is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term such rabbits breed initially and the warren has rabbits after months, then when is doomsday? because the exponent in the expression Let c be a positive number.A differential equation of the form where is a positive constant is called a because the exponent in the expression is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term such rabbits breed initially and the warren has rabbits after months, then when is doomsday? is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term Let c be a positive number.A differential equation of the form where is a positive constant is called a because the exponent in the expression is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term such rabbits breed initially and the warren has rabbits after months, then when is doomsday? such rabbits breed initially and the warren has Let c be a positive number.A differential equation of the form where is a positive constant is called a because the exponent in the expression is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term such rabbits breed initially and the warren has rabbits after months, then when is doomsday? rabbits after months, then when is doomsday?

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Question 56

Solve the differential equation. Solve the differential equation.

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Question 57

A common inhabitant of human intestines is the bacterium A common inhabitant of human intestines is the bacterium A cell of this bacterium in a nutrient-broth medium divides into two cells every The initial population of a culture is cells.Find the number of cells after hours. A cell of this bacterium in a nutrient-broth medium divides into two cells every A common inhabitant of human intestines is the bacterium A cell of this bacterium in a nutrient-broth medium divides into two cells every The initial population of a culture is cells.Find the number of cells after hours. The initial population of a culture is A common inhabitant of human intestines is the bacterium A cell of this bacterium in a nutrient-broth medium divides into two cells every The initial population of a culture is cells.Find the number of cells after hours. cells.Find the number of cells after A common inhabitant of human intestines is the bacterium A cell of this bacterium in a nutrient-broth medium divides into two cells every The initial population of a culture is cells.Find the number of cells after hours. hours.

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Question 58

Consider a population Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition with constant relative birth and death rates Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition and Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition respectively, and a constant emigration rate Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition , where Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition Then the rate of change of the population at time Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition is modeled by the differential equation Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition where Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition Find the solution of this equation with the rate of change of the population at time Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition that satisfies the initial condition Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition

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Question 59

Solve the differential equation. Solve the differential equation.

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Question 60
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