Deck 6: Slope Fields and Eulers Method

Question 1

A)32
B)1
C)8
D)64
E)16

Answer 1

B

Question 2

integration to find a general solution of the differential equation.

Answer 2

C

Question 3

Answer 3

D

Question 4

integration to find a general solution of the differential equation .

Question 5

integration to find a general solution of the differential equation.

Question 6

Question 7

Question 8

Select from the choices below the slope field for the differential equation.

Question 9

Question 10

integration to find a general solution of the differential equation

Question 11

Question 12

Question 13

Solve the differential equation.

Question 14

Question 15

Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.15.

Question 16

Select from the choices below the slope field for the differential equation.

Question 17

integration to find a general solution of the differential equation.

Question 18

Question 19

integration to find a general solution of the differential equation.

Question 20

Select from the choices below the slope field for the differential equation.

Question 21

Question 22

initial investment in a savings account in which interest is compounded

Question 23

the isotope is reduced 1.6 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 1,000 years? Round your answers to four decimal places.

A)2.1332 , 2.0727
B)2.7731 , 2.6945
C)1.2799 , 1.2436
D)1.7065 , 1.6582
E)1.0666 , 1.0364

Question 24

Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four
Decimal places:

Question 25

Question 26

initial investment in a savings account in which interest is compounded

Question 27

the time (in years) necessary for 1,000 to double if it is invested at a rate 6% compounded continuously. Round your answer to two decimal places.

A)1.16 years
B)11.55 years
C)1.39 years
D)11.90 years
E)11.58 years

Question 28

Solve the differential equation.

Question 29

the principal that must be invested at the rate 8%, compounded monthly, so that $1,000,000 will be available for retirement in 50 years. Round your answer to the nearest cent.

A)$250,000.00
B)$18,560.39
C)$717,324.37
D)$333,333.33
E)$21,321.23

Question 30

Write and solve the differential equation that models the following verbal statement:

Question 31

half-life of the radium isotope Ra-226 is approximately 1,599 years. What percent of a given amount remains after 800 years? Round your answer to two decimal places.

A)70.70 %
B)5.71 %
C)72.70 %
D)25.02 %
E)0.71 %

Question 32

Question 33

Solve the differential equation.

Question 34

Question 35

Question 36

half life of the radium isotope Ra-226 is approximately 1,599 years. If the amount left after 1,000 years is 1.8 g, what is the amount after 2000 years? Round your answer to
Three decimal places.

A)1.167 g
B)0.939 g
C)1.800 g
D)0.490 g
E)2.334 g

Question 37

Question 38

Solve the differential equation.

Question 39

Question 40

Question 41

Question 42

the largest value of b?

Question 43

Question 44

Question 45

the smallest value of b?

Question 46

the orthogonal trajectories of the family

Question 47

Question 48

number of bacteria in a culture is increasing according to the law of exponential growth. After 5 hours there are 175 bacteria in the culture and after 10 hours there are 425 bacteria in

Question 49

Suppose that the population (in millions) of a Egypt in 2007 is 80.3 and that expected

Question 50

Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically.

Question 51

Question 52

Question 53

Question 54

Suppose that the population (in millions) of Paraguay in 2007 was 6.7 and that the

Question 55

container of hot liquid is placed in a freezer that is kept at a constant temperature

Question 56

Identify the value of k.

A)1.7
B)2.2
C)0.2
D)20
E)0.5

Question 57

Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically.

Question 58

an equation of the graph that passes through the point (7, 3) and has the slope

Question 59

Question 60

Question 61

conservation organization releases 50 foxes into a preserve. After 5 years, there are 85 foxes in the preserve. The preserve has a carrying capacity of 225. Determine the population after
10 years. Discard any fractional part of your answer.

A)126
B)118
C)139
D)131
E)205

Question 62

conservation organization releases coyotes into a preserve. After years, 40 4
There are
70 coyotes in the preserve. The preserve has a carrying capacity of 175. Write a logistic
Function that models the population of coyotes in the preserve.

Question 63

the particular solution of the differential equation

Question 64

Identify the maximum carrying capacity.

A)20
B)1.7
C)0.5
D)0.2
E)2.2

Question 65

Match the logistic differential equation and initial condition with the graph of its solution shown below.

Question 66

Question 67

the initial population.

A)6
B)8
C)3
D)24
E)2

Question 68

the logistic equation that satisfies the following differential equation and initial

Question 69

conservation organization releases 30 panthers into a preserve. After 3 years, there are 50 panthers in the preserve. The preserve has a carrying capacity of 150. Determine the time it
Takes for the population to reach 110.

A)13.139 years
B)8.994 years
C)10.378 years
D)7.811 years
E)12.003 years

Question 70

Match the logistic equation and initial condition with the graph of the solution.

Question 71

Question 72

the particular solution of the differential equation

Question 73

Solve the first order linear differential equation.

Question 74

Question 75

Determine when the population reaches of the maximum carrying capacity. Round your answer to three decimal places.

A)4.317
B)3.000
C)0.474
D)0.677
E)0.301

Question 76

the particular solution of the differential equation

Question 77

Determine when the population reaches one-half of the maximum carrying capacity. Round your answer to three decimal places.

A)0.549
B)3.333
C)1.151
D)5.000
E)1.000

Question 78

300-gallon tank is full of a solution containing 35 pounds of concentrate. Starting at time distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred
Solution is withdrawn at the same rate. Find the amount of concentrate Q in the solution as a function
Of t.

Question 79

Solve the first order linear differential equation.

Question 80