Exam 9: Differential Equations

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

A population is modeled by the differential equation. For what values of P is the population increasing? Select the correct Answer

Consider a population with constant relative birth and death rates and respectively, and a constant emigration rate , where and Then the rate of change of the population at time is modeled by the differential equation where Find the solution of this equation with the rate of change of the population at time that satisfies the initial condition

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.Suppose that a roast turkey is taken from an oven when its temperature has reached and is placed on a table in a room where the temperature is is the temperature of the turkey after minutes, then Newton's Law of Cooling implies that This could be solved as a separable differential equation.Another method is to make the change of variable If the temperature of the turkey is after half an hour, what is the temperature after 35 min? Select the correct Answer

Find the solution of the initial-value problem and use it to find the population when

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

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

Select the correct Answer: for each question. -Which of the following functions is a solution of the differential equation? a. b. c. d. e.

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

Consider the differential equation as a model for a fish population, where is measured in weeks and is a constant.For what values of does the fish population always die out?

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

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

Select the correct Answer: for each question. -Let 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 is a positive constant.Solve it as a linear differential equation.

Solve the differential equation.

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

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?

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

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?

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?