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Deck 7: Extension G: Differential Equations
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Question
Solve the initial-value problem.
Question
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 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? Question
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 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). Question
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 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. Question
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, 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)
Question
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 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. Question
Solve the differential equation. 
A)
B)
C)
D)
E) none of these
A)
B)
C)
D)
E) none of these
Question
Choose the differential equation corresponding to this direction field. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the solution of the differential equation 
that satisfies the initial condition 
that satisfies the initial condition 
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Deck 7: Extension G: Differential Equations
1
Solve the initial-value problem.
2
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 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 3
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 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).
4
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 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. Unlock Deck
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5
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, 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)
Unlock Deck
Unlock for access to all 10 flashcards in this deck.
Unlock Deck
k this deck
6
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 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. Unlock Deck
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7
Solve the differential equation.
A)
B)
C)
D)
E) none of these
A)
B)
C)
D)
E) none of these
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8
Choose the differential equation corresponding to this direction field.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Find the solution of the differential equation that satisfies the initial condition
that satisfies the initial condition Unlock Deck
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