Exam 9: Differential Equations

Select the correct Answer: for each question. -We modeled populations of aphids and ladybugs with a Lotka-Volterra system.Suppose we modify those equations as follows: Find the equilibrium solution.

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

Solve the differential equation.

Solve the differential equation.

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

Solve the initial-value problem.

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

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

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

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.) Select the correct Answer

Find the orthogonal trajectories of the family of curves.

be a positive number.A differential equation of the form where is a positive constant is called because the exponent in the expression is larger than the exponent 1 for natural growth.An especially prolific breed of rabbits has the growth term If such rabbits breed initially and the warren has rabbits after months, then when is doomsday? Select the correct Answer

Select the correct Answer: for each question. -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.

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

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

An object with mass is dropped from rest and we assume that the air resistance is proportional to the speed of the object.If is the distance dropped after t seconds, then the speed is and the acceleration is .If g is the acceleration due to gravity, then the downward force on the object is where is a positive constant, and Newton's Second Law gives Find the limiting velocity.

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

Let What are the equilibrium solutions?

Select the correct Answer: for each question. -Which of the following functions are the constant solutions of the equation a. b. c. d. e.

Solve the initial-value problem.