Euler's Method and Logistic Growth

Let y=f(x)be the solution to the differential equation dy/dx=x+y with the initial condition f(1)=2. What is the approximation for f(2) if Euler’s method is used, starting at x=1with a step size of 0.5?

• 3

• 5

• 6

• 10

Given that y(1)=-3 and dy/dx=2x+y, what is the approximation for y(2) if Euler’s method is used with a step size of 0.5, starting at x=1?

• -4.25

• -4

• -3.75

• -3.5

Let y=f(x) be the particular solution to the differential equation dy/dx=x+2y with the initial condition f(0)=1. Use Euler’s method, starting at x=0 with two steps of equal size, to approximate f( 0.6).

• -0.25

• -0.55

• 0.55

• 0.25

Assume that f and f' have the values given in the table. Use Euler’s Method with two equal steps to approximate the value of f(4.4).

• 1.96

• 1.88

• 1.84

• 0.88

he number of moose in a national park is modeled by the function M that satisfies the logistic differential equation dM/dt=0.6M(1-(M/200)), where t is the time in years and M(0)=50. What is lim(t->infinity)M(t)?

• 50

• 200

• 500

• 1000

Which of the following differential equations for a population P could model the logistic growth shown in the figure above?

• (dP/dt)=0.2P-0.001P²

• (dP/dt)=0.1P-0.001P²

• (dP/dt)=0.2P²-0.001P

• (dP/dt)=0.1P²-0.001P

suppose a population of bears grows according to the logistic differential equation dP/dt=2P-0.01P² where P is the number of bears at time t in years. which of the following statements are TRUE?

the growth rate of the bear population is greatest at P=100 If P>200, the population of bears is decreasing. lim(t->infinity)P(t)=200

• 1 only

• 2 only

• 2 and 3 only

• 1, 2, and 3

which of the following differential equations is not logistic?

• P'=P-P^2

• dy/dx=0.01y(100-y)

• dx/dt=0.8x-0.004x^2

• dR/dt=0.16(350-R)

A puppy weighs 2 pounds at birth and 3.5 pounds two months later. If the weight fo the puppy during its first 6 months is increasing at a rate proportional to its wright, then how much will the puppy weigh it is 3 months old?

• 4.2 pounds

• 4.6 pounds

• 4.8 pounds

• 5.6 pounds

(calc active) water flows continuously from a large tank at a rate proportional to the amount of water remaining in the tank; that is dy/dt=ky. There was initially 10,000 cubic feet of water in the tank, and at the time t=4 hours, 8000 cubic feet remained. what is the value of of k in the equation dy/dt=ky?

• -0.050

• 0.169

• -0.056

• -0.200