Exam 9: Differential Equations

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).

Select the correct Answer: for each question. -A curve passes through the point and has the property that the slope of the curve at every point is times the y-coordinate What is the equation of the curve?

Use Euler's method with step size 0.25 to estim ate where is the solution of the initial-value problem.Round yourAnswer to four decimal places.

Determine whether the differential equation is linear.Select the correct Answer

Which equation does the function satisfy?

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

Solve the differential equation.Select the correct Answer

be the performance level of someone learning a skill as a function of the training time t.The graph of P is called a We propose the differential equation as a reasonable model for learning, where r is a positive constant.Solve it as a linear differential equation.

Solve the initial-value problem.

Solve the differential equation.

Solve the initial-value problem.

Solve the differential equation.

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

Select the correct Answer: for each question. -The population of the world was about 5.3 billion in 1990.Birth rates in the 1990s range from 35 to 40 million per year and death rates range from 15 to 20 million per year.Let's assume that the carrying capacity for world population is 100 billion.Use the logistic model to predict the world population in the 2,450 year.Calculate yourAnswer in billions to one decimal place.(Because the initial population is small compared to the carrying capacity, you can take to be an estimate of the initial relative growth rate.)

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

A function satisfies the differential equation What are the constant solutions of the equation?

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

Solve the differential equation.

Solve the differential equation.

Select a direction field for the differential equation from a set of direction fields labeled I-IV.