Exam 9: Differential Equations

In the circuit shown in Figure, a generator supplies a voltage of volts, the inductance is 2 H, the resistance is 40 and Find the current 0.2 s after the switch is closed.Round yourAnswer to two decimal places.

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

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.)

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.

Solve the initial-value problem.

Which equation does the function satisfy?

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 Find the number of cells after

Solve the differential equation.

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 is a positive constant.Solve it as a linear differential equation.

Select the correct Answer: for each question. -For what values of does the function atisfy the differential equation a. b. c. d. e.

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

Solve the initial-value problem.Select the correct Answer

Solve the initial-value problem.

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

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

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

Solve the differential equation.

Solve the initial-value problem.

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 If is the temperature of the turkey after t 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?

Solve the initial-value problem.