Question 1

Use integration to find a general solution of the differential equation

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    B

Question 2

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

Accepted Answer

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

Question 3

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.

Accepted Answer

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

Question 4

Identify the slope field of the differential equation

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Solve the differential equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Solve the differential equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

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.

Accepted Answer

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

Question 10

Which of the following is a solution of the differential equation

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

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.

Accepted Answer

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

Question 12

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.

Accepted Answer

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 
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 13

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

Accepted Answer

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

Question 14

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.

Accepted Answer

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

Question 15

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.

Accepted Answer

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

Question 16

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Find the function   passing through the point   with the first derivative

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Use integration to find a general solution of the differential equation

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

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.

Identify the slope field of the differential equation

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

Solve the differential equation.

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

Solve the differential equation.

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.

Which of the following is a solution of the differential equation

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.

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.

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

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.

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

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

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.

Find the function passing through the point with the first derivative

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

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

Filters

Exam 6: Differential Equations

Use integration to find a general solution of the differential equation

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

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.

Identify the slope field of the differential equation

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

Solve the differential equation.

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

Solve the differential equation.

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.

Which of the following is a solution of the differential equation

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.

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.

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

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.

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

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

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.

Find the function passing through the point with the first derivative

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

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

Filters