Question 1

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

Accepted Answer

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

Question 2

The isotope   has a half-life of 24,100 years.Given an initial amount of 6 grams of the isotope,how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places. ​

Accepted Answer

A) 4.1400 g,3.6374 g 
B) 3.5486 g,3.1178 g 
C) 5.9143 g,5.1963 g 
D) 2.3657 g,2.0785 g 
E) 7.0972 g,6.2356 g 
A) 4.1400 g,3.6374 g 
B) 3.5486 g,3.1178 g 
C) 5.9143 g,5.1963 g 
D) 2.3657 g,2.0785 g 
E) 7.0972 g,6.2356 g

Question 3

The number of bacteria in a culture is increasing according to the law of exponential growth.After 5 hours there are 130 bacteria in the culture and after 10 hours there are 330 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 10,000?
​

Accepted Answer

A) (I)51.2121 ; (II)   ; (III)3,439.1838 ; (IV)30.6439 hr 
B) (I)53.3621 ; (II)   ; (III)4,813.9010 ; (IV)32.8719 hr 
C) (I)51.2121 ; (II)   ; (III)2,126.4497 ; (IV)28.3094 hr 
D) (I)56.9921 ; (II)   ; (III)7,565.3544 ; (IV)34.9831 hr 
E) (I)58.5521 ; (II)   ; (III)10,217.8179 ; (IV)36.7625 hr 
A) (I)51.2121 ; (II)   ; (III)3,439.1838 ; (IV)30.6439 hr 
B) (I)53.3621 ; (II)   ; (III)4,813.9010 ; (IV)32.8719 hr 
C) (I)51.2121 ; (II)   ; (III)2,126.4497 ; (IV)28.3094 hr 
D) (I)56.9921 ; (II)   ; (III)7,565.3544 ; (IV)34.9831 hr 
E) (I)58.5521 ; (II)   ; (III)10,217.8179 ; (IV)36.7625 hr

Question 4

Consider the differential equation ​   ,for ​   only,with initial value   .
​
The particular solution y(x)is
​

Accepted Answer

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

Question 5

Find the logistic equation that satisfies the following differential equation and initial condition. ​   ​

Accepted Answer

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

Question 6

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?
​

Accepted Answer

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

Question 7

A conservation organization releases 40 coyotes into a preserve.After 4 years,there are 70 coyotes in the preserve.The preserve has a carrying capacity of 175.Determine the time it takes for the population to reach 140. ​

Accepted Answer

A) 15.599 years 
B) 11.454 years 
C) 12.838 years 
D) 10.271 years 
E) 14.463 years 
A) 15.599 years 
B) 11.454 years 
C) 12.838 years 
D) 10.271 years 
E) 14.463 years

Question 8

The logistic function   models the growth of a population.Identify the initial population. ​

Accepted Answer

A) 10 
B) 12 
C) 5 
D) 60 
E) 6 
A) 10 
B) 12 
C) 5 
D) 60 
E) 6

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

The isotope has a half-life of 24,100 years.Given an initial amount of 6 grams of the isotope,how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places.

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

Find the logistic equation that satisfies the following differential equation and initial condition.

A conservation organization releases 40 coyotes into a preserve.After 4 years,there are 70 coyotes in the preserve.The preserve has a carrying capacity of 175.Determine the time it takes for the population to reach 140.

The logistic function models the growth of a population.Identify the initial population.

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

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

The isotope has a half-life of 24,100 years.Given an initial amount of 6 grams of the isotope,how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places. ​

Consider the differential equation ​ ,for ​ only,with initial value . ​ The particular solution y(x)is ​

Find the logistic equation that satisfies the following differential equation and initial condition. ​ ​