Question 1

Solve the differential equation. ​   ​

Accepted Answer

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

Question 2

The logistic function   models the growth of a population.Determine when the population reaches 40% of the maximum carrying capacity.Round your answer to three decimal places. ​

Accepted Answer

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

Question 3

Determine whether the function   is homogeneous and determine its degree if it is. ​

Accepted Answer

A) homogeneous,the degree is 3 
B) homogeneous,the degree is 4 
C) not homogeneous00 
D) homogeneous,the degree is 2 
E) homogeneous,the degree is 1 
A) homogeneous,the degree is 3 
B) homogeneous,the degree is 4 
C) not homogeneous00 
D) homogeneous,the degree is 2 
E) homogeneous,the degree is 1

Question 4

​Consider the differential equation ​   ,for ​   only,with initial value   .
​
Using Euler's Method with step size   ,what is the estimate for   ?
​

Accepted Answer

A) ​   
B) ​2.5 
C) ​3 
D) ​4.85 
A) ​   
B) ​2.5 
C) ​3 
D) ​4.85

Question 5

The general solution to the differential equation   is ​​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 6

Solve the differential equation. ​   ​

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Show that   .​

Accepted Answer

The answer of Show that   .​...

Question 9

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

Accepted Answer

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

Question 10

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 N is proportional to N.When   ,   and when   ,   .What is the value of N when   ?
​

Accepted Answer

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

Question 11

Solve the homogeneous differential equation   . ​

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Solve the differential equation. ​   ​

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

Question 16

If   then the particular solution   is​ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 17

The half-life of the radium isotope Ra-226 is approximately 1,599 years.What percent of a given amount remains after 100 years? Round your answer to two decimal places. ​

Accepted Answer

A) 95.76 % 
B) 5.96 % 
C) 97.76 % 
D) 3.13 % 
E) 0.96 % 
A) 95.76 % 
B) 5.96 % 
C) 97.76 % 
D) 3.13 % 
E) 0.96 %

Question 18

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. ​

Accepted Answer

A) 103.5 
B) 100.4 
C) 101.9 
D) 108.7 
E) 96.4 
A) 103.5 
B) 100.4 
C) 101.9 
D) 108.7 
E) 96.4

Question 19

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
​

Accepted Answer

A) ​176 
B) ​358 
C) ​353 
D) ​349 
A) ​176 
B) ​358 
C) ​353 
D) ​349

Question 20

Suppose that the population (in millions)of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003.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)

Solve the differential equation.

The logistic function models the growth of a population.Determine when the population reaches 40% of the maximum carrying capacity.Round your answer to three decimal places.

Determine whether the function is homogeneous and determine its degree if it is.

Consider the differential equation ,for only,with initial value . Using Euler's Method with step size ,what is the estimate for ?

The general solution to the differential equation is

Solve the differential equation.

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

Show that .

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

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 N is proportional to N.When , and when , .What is the value of N when ?

Solve the homogeneous differential equation .

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

Solve the differential equation.

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

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.

If then the particular solution is

The half-life of the radium isotope Ra-226 is approximately 1,599 years.What percent of a given amount remains after 100 years? Round your answer to two decimal places.

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.

Suppose that the population (in millions)of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003.Find the exponential growth model for the population by letting correspond to 2000.Round your answer to four decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 6: Differential Equations

Solve the differential equation. ​ ​

The logistic function models the growth of a population.Determine when the population reaches 40% of the maximum carrying capacity.Round your answer to three decimal places. ​

Determine whether the function is homogeneous and determine its degree if it is. ​

​Consider the differential equation ​ ,for ​ only,with initial value . ​ Using Euler's Method with step size ,what is the estimate for ? ​

The general solution to the differential equation is ​​

Solve the differential equation. ​ ​

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

Show that .​

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

Solve the homogeneous differential equation . ​

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

Solve the differential equation. ​ ​

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

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. ​

If then the particular solution is​ ​

The half-life of the radium isotope Ra-226 is approximately 1,599 years.What percent of a given amount remains after 100 years? Round your answer to two decimal places. ​

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. ​

Suppose that the population (in millions)of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003.Find the exponential growth model for the population by letting correspond to 2000.Round your answer to four decimal places. ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Solve the differential equation.

The logistic function models the growth of a population.Determine when the population reaches 40% of the maximum carrying capacity.Round your answer to three decimal places.

Determine whether the function is homogeneous and determine its degree if it is.

Consider the differential equation ,for only,with initial value . Using Euler's Method with step size ,what is the estimate for ?

The general solution to the differential equation is

Solve the differential equation.

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

Show that .

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

Solve the homogeneous differential equation .

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

Solve the differential equation.

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

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.

If then the particular solution is

The half-life of the radium isotope Ra-226 is approximately 1,599 years.What percent of a given amount remains after 100 years? Round your answer to two decimal places.

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.

Suppose that the population (in millions)of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003.Find the exponential growth model for the population by letting correspond to 2000.Round your answer to four decimal places.