Test Bank Brief Calculus for the Business, Social and Life Sciences 3rd Edition by Bill Armstrong

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Test Bank Brief Calculus for the Business, Social and Life Sciences 3rd Edition by Bill Armstrong

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Test Bank Brief Calculus for the Business, Social and Life Sciences 3rd Edition by Bill Armstrong

File: chap1, Chapter 1

 

Multiple Choice

  1. Make a scatterplot of the tabular data.
   

0

1

2

 

1

2

 

0

 

A.

B.

C.

D.

 

ANS: A

Page: Section 1.1

 

 

 

  1. What is the domain of the function using interval notation?

 

  1.  
  2.  
  3.  
  4.  

 

ANS:  B

 Page: Section 1.1

 

 

 

  1. Find the domain D and range R of the following function using interval notation.

 

  1.  
  2.  
  3.  
  4.  

 

ANS: D

Page: Section 1.1

 

 

 

  1. Classify the function as increasing or decreasing and identify the slope of the line.

 

  1. Decreasing,
  2. Increasing,
  3. Increasing, 17.1
  4. Decreasing,

 

ANS: D

Page: Section 1.2

 

 

 

  1. Use the ZERO command on your calculator to approximate the zeros of the quadratic function . Round your answer to the nearest hundredth. 

 

  1.  
  2.  
  3.  
  4.  

 

ANS: B

Page: Section 1.3

 

 

 

  1. For the function and , evaluate .

 

  1.  
  2.  
  3.  
  4.  

 

ANS: C

Page:  Section 1.4

 

 

 

  1. Determine the end behavior of the function  as  and as .

 

  1. As , ; as ,
  2. As ; as
  3. As ; as
  4. As ; as

 

ANS: B

Page: Section 1.4

 

 

 

  1. Determine the functions f and g such that given .  There may be more than one correct answer.

 

  1.  
  2.  
  3.  
  4.  

 

ANS:  B, C, or D

Page: Section 1.4

 

 

 

  1. Form a rational function, keeping the numerator and denominator factored, which meets all of the following requirements:

(i)  There is a hole at

(ii)  There are x-intercepts at  and

(iii)  There are vertical asymptotes at  and

(iv)  There is a horizontal asymptote at

 

  1.  
  2.  
  3.  
  4.  

 

ANS: C or D

Page: Section 1.5

 

 

 

True or False

 

 

 

  1. The table represents a function.

Domain

Range

-3

-5

-2

4

0

8

2

6

5

4

 

 

 

 

 

 

 

ANS: True

Page: Section 1.1

 

 

 

  1. Determine if the following statement is true or false. If false, rewrite the statement so that it is true: The polynomial function is a second-degree polynomial function.

 

ANS: False.  The function is a third-degree polynomial function.

Page: Section 1.4

 

 

 

  1. Determine if the following statement is true or false. If false, rewrite the statement so that is it true:

The rational function  will have a hole at  and a vertical asymptote at .

 

ANS: True

Page:  Section 1.5

 

 

 

  1. Determine if the following statement is true or false. If false, rewrite the statement so that is it true:

The rational function  will have a horizontal asymptote at .

 

ANS: True

Page:  Section 1.5

 

 

 

Short Answer

 

 

 

  1. For the function , find…

(a) 

(b) 

(c) 

 

ANS:  (a) -1

(b)  1

(c)  41

Page: Section 1.1

 

 

 

  1. Let be the number of years since 1980.  Standardize the value of the independent variable based on its definition and make a scatterplot of the data.  (Source: U. S. Census Bureau.) 

Year

Per Capita Consumption of Whole Milk (in gallons)

1980

17.0

1990

10.5

1995

8.6

2000

8.1

2005

7.0

2006

6.7

2007

6.4

2008

6.1

2009

5.9

 

ANS:

Year

Per Capita Consumption of Whole Milk (in gallons)

0

17.0

10

10.5

15

8.6

20

8.1

25

7.0

26

6.7

27

6.4

28

6.1

29

5.9

 

Page: Section 1.1

 

 

 

Short Answer

 

 

 

  1. For the function , find the average rate of change between  and .

 

ANS: 5

Page: Section 1.2

 

 

 

  1. Write the slope-intercept form of the equation of the line with a y-intercept at 7 and that passes through the point .

 

ANS:

Page: Section 1.2

 

 

 

  1. A new machine costs $450,000 and depreciates at the rate of $17,500 per year. Determine the equation of the depreciation function f after x years.

 

ANS:

Page: Section 1.2

 

 

 

  1. It was found that the cost to improve and maintain the national parks of the U. S. can be approximated by the function where x is the number of years since 2000 and f is in millions of dollars and .  (Source: U. S. Census Bureau.) 

 

(a)  Interpret the y-intercept of the function.

(b)  Evaluate  and interpret the result.

(c)  According to the model, during what year did the costs reach $400,000,000?

 

ANS: (a)  In 2000, the approximate cost to improve and maintain the national parks of the U.S. was 287.80 million dollars.

(b)  424.28. In 2008, the approximate cost to improve and maintain the national parks of the U.S. was 424.28 million dollars.

(c)  During 2006, the costs reached $400,000,000.

Page: Section 1.2

 

 

 

  1. The cost to produce each cookie was 25 cents with $20.28 being spent for the supplies. Identify the variable and fixed costs for this scenario and write the corresponding cost function, C, where x is the number of cookies produced.

 

ANS: Variable costs $0.25; Fixed costs $20.28; Cost function

Page: Section 1.2

 

 

 

  1. For the function , find the vertex algebraically and determine the interval where the function is increasing and where the function is decreasing.

 

ANS:  Vertex: ; Increasing ; Decreasing

Page: Section 1.3

 

 

 

  1. A ball is tossed into the air and follows a path given by where s is height in feet and t is time in seconds since the ball was tossed.  Determine the average rate of change of the height of the ball from the  to and interpret.

 

ANS: 20;  The height of the ball is increasing by 20 feet per second from the 1st to the 4th second.

Page: Section 1.3

 

 

 

  1. From March 2012 to August 2012, the price per barrel of crude oil, in U. S. dollars, can be modeled by the function where x represents the number of months since February 1st, .  (Source:  U.S. Energy Information Administration.)

(a)  Determine the vertex of the function rounded to two decimal places.  Convert the x-coordinate to Month/Day format and interpret each coordinate of the vertex.

(b) Determine the average rate of change of the prices per barrel, rounded to two decimal places, from  to  and interpret.

 

ANS: (a) The vertex is located at ; Around June 12th, the price per barrel reached a minimum of around $87.83.

(b)  ;  The price per barrel was decreasing by about $1.57 per month from May to July 2012.

Page: Section 1.3

 

 

 

  1. Michele has studied weekly sales of gelato and pizzelles in his bakery. He found the weekly profit, in dollars, from gelato sales is given by  and the weekly profit, also in dollars, from pizzelle sales is given by  where x is the number of weeks since his business opened and .

(a)  Evaluate  and interpret.

(b)  Evaluate  and interpret.

(c)  Determine the total profit after 5 weeks.

 

ANS: (a)  612.64;  The profit after 8 weeks was $612.64.

(b)  230.3; After 10 weeks, the profit from gelato sales was $230.30 greater than the profit from pizzelle sales.

(c) $559.90.

Page:  Section 1.4

 

 

 

  1. In January 2010, it was determined that the parts required to produce each Playstation 3 by Sony cost $336.27. (Source: DLB-Network.) The Playstation 3 sold for $599 at launch and assume the fixed costs for labor, manufacturing, and advertising were $100,000,000. Let  represent the number of Playstation 3’s produced and sold.

(a)  Determine the associated cost function, C.

(b)  Determine the associated revenue function, R.

(c)  Determine the number of Playstation 3’s that are necessary to sell for Sony to break-even.  Round answer to the nearest whole number.

 

ANS: (a)

(b)

(c) 

Page: Section 1.4

 

 

 

  1. For the function . Find the following:

(a)  The domain

(b)  The x-intercept(s)

(c)  The y-intercept

(d)  The location of any vertical asymptotes or holes

(e)  The location of any horizontal asymptotes

 

ANS: (a)

(b) 

(c) 

(d)  Vertical asymptote at ; Hole at

(e) 

Page: Section 1.5

 

 

 

  1. The amount spent on salaries and wages for employees in the U.S. national park system can be modeled by the power function where x is the number of years since 1989 and f is the cost in millions of dollars and . (Source: U. S. Census Bureau.) 

(a)  Find  and interpret its meaning.

(b)  Compute  for  and  and interpret its meaning.  Round to three decimal places.

 

ANS: (a) 427.573;  In 1990, the approximate amount spent on salaries and wages for employees in the U.S. national park system was approximately $427,573,000.

(b) 44.191; From 1990 to 2000, the amount spent on salaries and wages for employees in the U.S. national park system was increasing by about $44,191,000 per year.

Page:  Section 1.5

 

 

 

  1. Match the function with its real zeros.

 

__ 

__ 

__ 

__ 

 

  1.  
  2.  
  3.  
  4.  

 

ANS: C; A; D; B

Page: Section 1.3

 

 

 

  1. For the functions and , match the domains of the given functions.  Note that some answers may be used more than once as needed and not all answers will be used.

 

___ 

___ 

___ 

___ 

 

  1.  
  2.  
  3.  
  4.  

 

ANS: D; D; A; C

Page: Section 1.4

 

 

 

  1. Match the function below to its domain. Answers may be used more than once.

 

___

___

___

___

 

  1.  
  2.  
  3.  
  4.  

 

ANS:  C; A; B; D

Page: Section 1.5

 

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