Question 1

At the minimum value, a valley, for a function   , the rate of change   is 0.

Accepted Answer

A) True 
 B)False

Question 2

The amount L, in liters, of liquid remaining in a tank after t hours satisfies the equation of change   .How much liquid is in the tank after a long time? ​

Accepted Answer

A)  6 liters 
B)  42 liters 
C)  1.17 liters 
D)  7 liters 
A)  6 liters 
B)  42 liters 
C)  1.17 liters 
D)  7 liters

Question 3

Find the equilibrium solution of the equation of change   .Round your answer to two decimal places, if nessary. ​

Accepted Answer

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

Question 4

A certain population grows according to an equation of change.What can be said of population growth when the population level is at a steady state solution of the equation of change? ​

Accepted Answer

A)  The population is stable--neither increasing nor decreasing. 
B)  The population is increasing. 
C)  The population is decreasing. 
D)  There is not sufficient information to determine how population grows. 
A)  The population is stable--neither increasing nor decreasing. 
B)  The population is increasing. 
C)  The population is decreasing. 
D)  There is not sufficient information to determine how population grows.

Question 5

Equilibrium or steady-state solutions for an equation of change are solutions that remain constant.

Accepted Answer

A) True 
 B)False

Question 6

The weight w, in pounds of a certain animal at age t years satisfies the equation of change   .At what weight is the animal growing the fastest? Round your answer to two decimal places. ​

Accepted Answer

A)  0.47 pounds 
B)  2.13 pounds 
C)  1.06 pounds 
D)  None of the above 
A)  0.47 pounds 
B)  2.13 pounds 
C)  1.06 pounds 
D)  None of the above

Question 7

The weight w of a certain animal satisfies an equation of change.At a specific weight, the equation of change indicates that   is negative.What can you conclude about how the animal's weight can be expected to change? ​

Accepted Answer

A)  The weight will stay the same. 
B)  The animal will gain weight. 
C)  The animal will lose weight. 
D)  The weight is at a maximum value. 
A)  The weight will stay the same. 
B)  The animal will gain weight. 
C)  The animal will lose weight. 
D)  The weight is at a maximum value.

Question 8

Find the equilibrium solution of the equation of change   . ​

Accepted Answer

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

Question 9

A certain population grows according to   .At a certain time the population is 698 individuals.What can be said about the population at this time? ​

Accepted Answer

A)  The population is increasing. 
B)  The population is decreasing. 
C)  The population has reached a maximum value. 
D)  The population has reached a minimum value. 
A)  The population is increasing. 
B)  The population is decreasing. 
C)  The population has reached a maximum value. 
D)  The population has reached a minimum value.

Question 10

Find the equilibrium solutions of the equation of change   . ​

Accepted Answer

A)    and   
B)    and   
C)    and   
D)    and   
A)    and   
B)    and   
C)    and   
D)    and

Question 11

Find the equilibrium solutions of the equation of change   .Round your answer to two decimal places, if necessary. ​

Accepted Answer

A)    and   
B)    and   
C)    and   
D)    and   
A)    and   
B)    and   
C)    and   
D)    and

Question 12

A certain population grows according to   .At a certain time the population is 1,140 individuals.What can be said about the population at this time? ​

Accepted Answer

A)  The population is increasing. 
B)  The population is decreasing. 
C)  The population has reached a maximum value. 
D)  The population has reached a minimum value. 
A)  The population is increasing. 
B)  The population is decreasing. 
C)  The population has reached a maximum value. 
D)  The population has reached a minimum value.

Question 13

When   is negative, the function   is also negative.

Accepted Answer

A) True 
 B)False

Question 14

Find the equilibrium solution of the equation of change   . ​

Accepted Answer

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

Question 15

Consider the equation of change   .What can you say about the graph of f versus x when   ? ​

Accepted Answer

A)  The graph is increasing. 
B)  The graph is decreasing. 
C)  The graph reaches a maximum. 
D)  The graph reaches a minimum. 
A)  The graph is increasing. 
B)  The graph is decreasing. 
C)  The graph reaches a maximum. 
D)  The graph reaches a minimum.

Question 16

The carrying capacity is an equilibrium solution for the equation of change for logistic growth.

Accepted Answer

A) True 
 B)False

Question 17

The function   satisfies the equation of change   .For what values of f is the graph of f versus x decreasing? ​

Accepted Answer

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

Question 18

Find the equilibrium solution of the equation of change   .Consider only positive values of x. ​

Accepted Answer

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

Question 19

Consider the equation of change   .What can you say about the graph of f versus x when   ? ​

Accepted Answer

A)  The graph is increasing. 
B)  The graph is decreasing. 
C)  The graph reaches a maximum. 
D)  The graph reaches a minimum. 
A)  The graph is increasing. 
B)  The graph is decreasing. 
C)  The graph reaches a maximum. 
D)  The graph reaches a minimum.

Exam 31: Equations of Change Graphical Solutions

At the minimum value, a valley, for a function , the rate of change is 0.

The amount L, in liters, of liquid remaining in a tank after t hours satisfies the equation of change .How much liquid is in the tank after a long time? ​

Find the equilibrium solution of the equation of change .Round your answer to two decimal places, if nessary. ​

A certain population grows according to an equation of change.What can be said of population growth when the population level is at a steady state solution of the equation of change? ​

Equilibrium or steady-state solutions for an equation of change are solutions that remain constant.

The weight w, in pounds of a certain animal at age t years satisfies the equation of change .At what weight is the animal growing the fastest? Round your answer to two decimal places. ​

The weight w of a certain animal satisfies an equation of change.At a specific weight, the equation of change indicates that is negative.What can you conclude about how the animal's weight can be expected to change? ​

Find the equilibrium solution of the equation of change . ​

A certain population grows according to .At a certain time the population is 698 individuals.What can be said about the population at this time? ​

Find the equilibrium solutions of the equation of change . ​

Find the equilibrium solutions of the equation of change .Round your answer to two decimal places, if necessary. ​

A certain population grows according to .At a certain time the population is 1,140 individuals.What can be said about the population at this time? ​

When is negative, the function is also negative.

Find the equilibrium solution of the equation of change . ​

Consider the equation of change .What can you say about the graph of f versus x when ? ​

The carrying capacity is an equilibrium solution for the equation of change for logistic growth.

The function satisfies the equation of change .For what values of f is the graph of f versus x decreasing? ​

Find the equilibrium solution of the equation of change .Consider only positive values of x. ​

Consider the equation of change .What can you say about the graph of f versus x when ? ​

Functions Given by Formulas

Functions Given by TableChas

Functions Given by Graphs

Functions Given by Words

Table and Trends

Graphs

Solving Linear Equations

Solving Nonlinear Equations

Inequalities

Optimization

The Geometry of Lines

Linear Functions

Modeling Data with Linear Functions

Linear Regression

Systems of Equations

Exponential Growth and Decay

Constant Percentage Change

Modeling Exponential Data

Modeling Nearly Exponential Data

Logarithmic Functions

Logistic Functions

Power Functions

Modeling Data with Power Functions

Combining and Decomposing Functions

Quadratic Functions

Higher Degree Polynomials and Rational Functions

Velocity

Rates of Change for Other Functions

Estimating Rates of Change

Equations of Change Linear and Exponential Functions

Filters

The amount L, in liters, of liquid remaining in a tank after t hours satisfies the equation of change .How much liquid is in the tank after a long time?

Find the equilibrium solution of the equation of change .Round your answer to two decimal places, if nessary.

A certain population grows according to an equation of change.What can be said of population growth when the population level is at a steady state solution of the equation of change?

The weight w, in pounds of a certain animal at age t years satisfies the equation of change .At what weight is the animal growing the fastest? Round your answer to two decimal places.

The weight w of a certain animal satisfies an equation of change.At a specific weight, the equation of change indicates that is negative.What can you conclude about how the animal's weight can be expected to change?

Find the equilibrium solution of the equation of change .

A certain population grows according to .At a certain time the population is 698 individuals.What can be said about the population at this time?

Find the equilibrium solutions of the equation of change .

Find the equilibrium solutions of the equation of change .Round your answer to two decimal places, if necessary.

A certain population grows according to .At a certain time the population is 1,140 individuals.What can be said about the population at this time?

Find the equilibrium solution of the equation of change .

Consider the equation of change .What can you say about the graph of f versus x when ?

The function satisfies the equation of change .For what values of f is the graph of f versus x decreasing?

Find the equilibrium solution of the equation of change .Consider only positive values of x.

Consider the equation of change .What can you say about the graph of f versus x when ?