# extenssion

Education

18

All Questions

14

Multiple Choice

0

True False

4

Essay

0

Short Answer

0

Not Answered

Q 1

The general solution to the differential equation is
A)
B)
C)
D)

Free

Multiple Choice

D

Q 2

If then the particular solution is
A)
B)
C)
D)

Free

Multiple Choice

B

Q 3

Consider the differential equation ,for only,with initial value .
Which of the following is the slope field for the general solution to the given differential equation?
A)
B)
C)
D)

Free

Multiple Choice

B

Q 4

Consider the differential equation ,for only,with initial value .
Using Euler's Method with step size ,what is the estimate for ?
A)
B)2.5
C)3
D)4.85

Multiple Choice

Q 5

Consider the differential equation ,for only,with initial value .
The particular solution y(x)is
A)
B)
C)
D)

Multiple Choice

Q 6

Water flows continuously from a large tank at a rate proportional to the amount of water remaining in the tank;that is, .There was initially 9,000 cubic feet of water in the tank,and at time hours,8,000 cubic feet of water remained.
What is the value of k in the equation ? Round your answer to 3 decimal places.
A)0.014
B)0.060
C)-0.131
D)-0.059

Multiple Choice

Q 7

Water flows continuously from a large tank at a rate proportional to the amount of water remaining in the tank;that is, .There was initially 10,000 cubic feet of water in the tank,and at time hours,6,000 cubic feet of water remained.
To the nearest cubic foot,how much water remained in the tank at time hours?
A)4,937
B)5,170
C)5,394
D)4,891

Multiple Choice

Q 8

A population of rabbits in a certain habitat grows according to the differential equation where t is measured in months and y is measured in hundreds of rabbits.There were initially 100 rabbits in this habitat;that is, .
What is the fastest growth rate,in rabbits per month,that this population exhibits?
A)150
B)600
C)300
D)250

Multiple Choice

Q 9

A population of rabbits in a certain habitat grows according to the differential equation where t is measured in months and y is measured in hundreds of rabbits.There were initially 100 rabbits in this habitat;that is, .
Which of the following slope fields represents an approximate general solution to the given differential equation?
A)
B)
C)
D)

Multiple Choice

Q 10

A population of rabbits in a certain habitat grows according to the differential equation where t is measured in months and y is measured in hundreds of rabbits.There were initially 100 rabbits in this habitat;that is, .
Estimates of y(t)can be produced using Euler's Method with step size .To the nearest rabbit,the estimate for y(2)is
A)176
B)358
C)353
D)349

Multiple Choice

Q 11

Water is being pumped continuously into a tank at a rate that is inversely proportional to the amount of water in the tank;that is, ,where y is the number of gallons of water in the tank after t minutes .Initially there were 5 gallons of water in the tank,and after 3 inutes there were 8 gallons.How many gallons of water were in the tank at time 20 minutes?
A)
B)
C)
D)

Multiple Choice

Q 12

Consider the differential equation ,for which the solution is .Let . The particular solution is
A)
B)
C)
D)

Multiple Choice

Q 13

Consider the differential equation ,for which the solution is g(x). Which of the following statements is true about the particular solution that contains (1,-4)?
A)g(x)is increasing and concave up.
B)g(x)is increasing and concave down.
C)g(x)is decreasing and concave up.
D)g(x)is decreasing and concave down.

Multiple Choice

Q 14

Consider the differential equation ,for which the solution is g(x). Let y(x)be the particular solution that contains (0,1).Using Euler's Method with step size ,what is the estimate for ?
A)4
B)3.5
C)3
D)4.5

Multiple Choice

Q 15

A differentiable function is defined such that,for all values of in its domain, .
-What is the domain of ?

Essay

Q 16

For what value(s)of x is ?

Essay

Q 17

Show that .

Essay

Q 18

Solve the differential equation in to find f(x)in terms of x only.

Essay