Deck 6: Differential Equations

Question 1

Use integration to find a general solution of the differential equation.

A)
B)
C)
D)
E)

Answer 1

Question 2

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

A)
B)
C)
D)none of the above

Answer 2

none of the above

Question 3

Identify the slope field of the differential equation

A)
B)
C)
D)
E)

Answer 3

Question 4

Use integration to find a general solution of the differential equation

A)
B)
C)
D)
E)

Question 5

Use the differential equation and its slope field to find the slope at the point

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

Question 6

Use integration to find a general solution of the differential equation.

A)
B)
C)
D)
E)

Question 7

Use integration to find a general solution of the differential equation.

A)
B)
C)
D)
E)

Question 8

Use 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.

A)
B)
C)
D)
E)

Question 9

Use integration to find a general solution of the differential equation .

A)
B)
C)
D)
E)

Question 10

Which of the following is a solution of the differential equation

A)
B)
C)
D)
E)

Question 11

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

A)
B)
C)
D)
E)none of the above

Question 12

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

A)
B)
C)
D)
E)none of the above

Question 13

Sketch the slope field for the differential equation and use the slope field to sketch the solution satisfying the condition

A)
B)
C)
D)
E)

Question 14

Which of the following is a solution of the differential equation

A)
B)
C)
D)
E)

Question 15

Sketch the slope field for the differential equation and use the slope field to sketch the solution that passes through the point

A)
B)
C)
D)
E)

Question 16

Find the particular solution of the differential equation that satisfies the initial condition is the general solution.

A)
B)
C)
D)
E)

Question 17

Which of the following is a solution of the differential equation

A)
B)
C)
D)
E)

Question 18

Use integration to find a general solution of the differential equation.

A)
B)
C)
D)
E)

Question 19

Use integration to find a general solution of the differential equation

A)
B)
C)
D)
E)

Question 20

Use integration to find a general solution of the differential equation.

A)
B)
C)
D)
E)

Question 21

Solve the differential equation.

A)
B)
C)
D)
E)

Question 22

At time minutes, the temperature of an object is The temperature of the object is changing at the rate given by the differential equation Use Euler's
Method to approximate the particular solutions of this differential equation at Use a step size of Round your answer to one decimal place.

A)96.6
B)99.9
C)102.9
D)98.1
E)97.4

Question 23

The a half-life of 5,715 years.After 2,000 years, a sample of the isotope is reduced to 1.2 grams.What was the initial size of the sample (in grams)? How much will
Remain after 20,000 years (i.e., after another 18000 years)? Round your answers to four decimal
Places.

A)1.0706 , 0.0947
B)2.4471 , 0.2164
C)1.5294 , 0.1352
D)2.1412 , 0.1893
E)1.9883 , 0.1758

Question 24

Solve the differential equation

A)
B)
C)
D)
E)

Question 25

Solve the differential equation.

A)
B)
C)
D)
E)

Question 26

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:
The rate of change of is proportional to .When and when What is the
Value of

A)
B)
C)
D)
E)

Question 27

Find the function passing through the point with the first derivative

A)
B)
C)
D)
E)

Question 28

The a half-life of 5,715 years.Given an initial amount of 11 grams of the isotope, how many grams will remain after 500 years? After 5,000 years? Round your answers to
Four decimal places.

A)7.2469 gm, 4.1988 gm
B)6.2117 gm, 3.5989 gm
C)10.3528 gm, 5.9982 gm
D)4.1411 gm, 2.3993 gm
E)12.4233 gm, 7.1979 gm

Question 29

The initial investment in a savings account in which interest is compounded continuously is $604.If the time required to double the amount is years, what is the amount after
15 years? Round your answer to the nearest cent.

A)$1,917.58
B)$1,804.46
C)$1,907.37
D)$1,404.46
E)$8,278.18

Question 30

Find the function passing through the point with the first derivative

A)
B)
C)
D)
E)

Question 31

Find the exponential function that passes through the two given points. Round your values of C and k to four decimal places.

A)
B)
C)
D)
E)

Question 32

The 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 33

The 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 34

The has a half-life of 24,100 years.After 10,000 years, a sample of 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 35

The rate of change of N is proportional to N.When and when What is the value of N when Round your answer to three decimal places.

A)2,129.520
B)2,099.520
C)2,049.520
D)491.383
E)262,440.000

Question 36

The initial investment in a savings account in which interest is compounded continuously is $813.If the time required to double the amount is years, what is the annual rate?
Round your answer to two decimal places.

A)7.49 %
B)7.70 %
C)13.34 %
D)6.29 %
E)8.89 %

Question 37

Write and solve the differential equation that models the following verbal statement: The rate of change of with respect to is proportional to

A)
B)
C)
D)
E)

Question 38

Solve the differential equation.

A)
B)
C)
D)
E)

Question 39

The half-life of the radium isotope Ra-226 is approximately 1,599 years.If the initial quantity of the isotope is 38 g, what is the amount left after 1,000 years? Round your answer to two
Decimal places.

A)24.63 g
B)30.60 g
C)25.13 g
D)11.88 g
E)12.32 g

Question 40

Solve the differential equation.

A)
B)
C)
D)
E)

Question 41

Find 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 42

Find 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 43

The 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
The culture.Answer the following questions, rounding numerical answers to four decimal places.
(i) Find the initial population.
(ii) Write an exponential growth model for the bacteria population.Let t represent time in hours.
(iii) Use the model to determine the number of bacteria after 20 hours.
(iv) After how many hours will the bacteria count be 15,000?

A)
B)
C)
D)
E)

Question 44

Suppose that the population (in millions) of Paraguay in 2007 was 6.7 and that the expected continuous annual rate of change of the population is 0.024.Find the exponential growth
Model for the population by letting correspond to 2000.Round your answer to four
Decimal places.

A)
B)
C)
D)
E)

Question 45

Suppose that the population (in millions) of a Egypt in 2007 is 80.3 and that expected continuous annual rate of change of the population is The exponential growth model for the population by letting corresponds to 2000 is Use the model to predict the
Population of the country in 2013.Round your answer to two decimal places.

A)83.08 million
B)87.42 million
C)90.45 million
D)88.92 million
E)81.68 million

Question 46

A container of hot liquid is placed in a freezer that is kept at a constant temperature of .The initial temperature of the liquid is After 3 minutes, the liquid's temperature is How much longer will it take for its temperature to decrease to Round your answer to
Two decimal places.

A)1.89 minutes
B)2.84 minutes
C)3.16 minutes
D)1.26 minutes
E)3.47 minutes