Exam 9: Differential Equations

Find the orthogonal trajectories of the family of curves.

A sum of s 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

Choose the differential equation corresponding to this direction field.

Solve the differential equation.

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? Select the correct Answer

In the circuit shown in Figure, a generator supplies a voltage of volts, the inductance is the resistance is 40 , and Find the current 0.2 s after the switch is closed.Round yourAnswer to two decimal places.

A curve passes through the point and has the property that the slope of the curve at every point P is times the y-coordinate P.What is the equation of the curve?

be the performance level of someone learning a skill as a function of the training time 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.

Suppose that a population develops according to the logistic equation where is measured in weeks.What is the carrying capacity? Select the correct Answer

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?

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? Select the correct Answer

Determine whether the differential equation is linear.

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 initial-value problem.

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

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

Solve the differential equation.

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

Solve the differential equation.Select the correct Answer

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.