Exam 7: Extension G: Differential Equations

Choose the differential equation corresponding to this direction field.

Find the solution of the differential equation that satisfies the initial condition

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.

Solve the differential equation.

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?

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 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).

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.

Solve the initial-value problem.

Solve the differential equation.