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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) A) and C)

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

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Solve the differential equation. Solve the differential equation.

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One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? inhabitants, One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? people have a disease at the beginning of the week and One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? have it at the end of the week. How long does it take for One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? of the population to be infected?

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A population is modeled by the differential equation. A population is modeled by the differential equation. For what values of P is the population increasing? A) B) C) D) E) For what values of P is the population increasing?


A) A population is modeled by the differential equation. For what values of P is the population increasing? A) B) C) D) E)
B) A population is modeled by the differential equation. For what values of P is the population increasing? A) B) C) D) E)
C) A population is modeled by the differential equation. For what values of P is the population increasing? A) B) C) D) E)
D) A population is modeled by the differential equation. For what values of P is the population increasing? A) B) C) D) E)
E) A population is modeled by the differential equation. For what values of P is the population increasing? A) B) C) D) E)

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

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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 t years. 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 t years. . 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 t years.

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The Pacific halibut fishery has been modeled by the differential equation The Pacific halibut fishery has been modeled by the differential equation where is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be and per year. If , find the biomass a year later. where The Pacific halibut fishery has been modeled by the differential equation where is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be and per year. If , find the biomass a year later. is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be The Pacific halibut fishery has been modeled by the differential equation where is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be and per year. If , find the biomass a year later. and The Pacific halibut fishery has been modeled by the differential equation where is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be and per year. If , find the biomass a year later. per year. If The Pacific halibut fishery has been modeled by the differential equation where is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be and per year. If , find the biomass a year later. , find the biomass a year later.

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A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let denote the amount of new currency in circulation at time t with . Formulate and solve a mathematical model in the form of an initial-value problem that represents the flow of the new currency into circulation (in billions per day). denote the amount of new currency in circulation at time t with A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let denote the amount of new currency in circulation at time t with . Formulate and solve a mathematical model in the form of an initial-value problem that represents the flow of the new currency into circulation (in billions per day). . Formulate and solve a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency into circulation (in billions per day).

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A tank contains A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after minutes? L of brine with A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after minutes? kg of dissolved salt. Pure water enters the tank at a rate of A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after minutes? L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after minutes? minutes?

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Choose the differential equation corresponding to this direction field. Choose the differential equation corresponding to this direction field. A) B) C) D) E)


A) Choose the differential equation corresponding to this direction field. A) B) C) D) E)
B) Choose the differential equation corresponding to this direction field. A) B) C) D) E)
C) Choose the differential equation corresponding to this direction field. A) B) C) D) E)
D) Choose the differential equation corresponding to this direction field. A) B) C) D) E)
E) Choose the differential equation corresponding to this direction field. A) B) C) D) E)

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

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One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction of the population who have heard the rumor and the fraction who have not heard the rumor. Let's assume that the constant of proportionality is One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction of the population who have heard the rumor and the fraction who have not heard the rumor. Let's assume that the constant of proportionality is . Write a differential equation that is satisfied by y. . Write a differential equation that is satisfied by y.

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Use Euler's method with step size 0.1 to estimate Use Euler's method with step size 0.1 to estimate , where is the solution of the initial-value problem. Round your answer to four decimal places. , where Use Euler's method with step size 0.1 to estimate , where is the solution of the initial-value problem. Round your answer to four decimal places. is the solution of the initial-value problem. Round your answer to four decimal places. Use Euler's method with step size 0.1 to estimate , where is the solution of the initial-value problem. Round your answer to four decimal places.

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

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


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

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

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One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E) inhabitants, One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E) people have a disease at the beginning of the week and One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E) have it at the end of the week. How long does it take for One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E) of the population to be infected?


A) One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E)
B) One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E)
C) One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E)
D) One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E)
E) One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of inhabitants, people have a disease at the beginning of the week and have it at the end of the week. How long does it take for of the population to be infected? A) B) C) D) E)

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

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Solve the differential equation. Solve the differential equation.

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For what values of k does the function For what values of k does the function satisfy the differential equation ? A) B) C) D) E) satisfy the differential equation For what values of k does the function satisfy the differential equation ? A) B) C) D) E) ?


A) For what values of k does the function satisfy the differential equation ? A) B) C) D) E)
B) For what values of k does the function satisfy the differential equation ? A) B) C) D) E)
C) For what values of k does the function satisfy the differential equation ? A) B) C) D) E)
D) For what values of k does the function satisfy the differential equation ? A) B) C) D) E)
E) For what values of k does the function satisfy the differential equation ? A) B) C) D) E)

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

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Let Let . What are the equilibrium solutions? . What are the equilibrium solutions?

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A sum of A sum of is invested at interest. If is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by . is invested at A sum of is invested at interest. If is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by . interest. If A sum of is invested at interest. If is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by . is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by A sum of is invested at interest. If is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by . .

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