Mathematical applications for the management life and social sciences 10th edition harshbarger test bank

Harshbarger/Reynolds, Mathematical Applications for the Management, Life, and Social Sciences, 10e Chapter 2 Quadratic and Other Special Functions 1... Harshbarger/Reynolds, Mathematica

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Harshbarger/Reynolds, Mathematical Applications for the Management, Life, and Social Sciences, 10e

Chapter 2 Quadratic and Other Special Functions

1 Write the equation 2 2

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5 Solve the equation by using the quadratic formula Give real solutions only

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9 Find the exact real solutions of the equation 2

x  x x , if they exist A) x5 and x 7

Ans: B

12 Solve the equation by using a graphing utility

2–14x105 7 x 0

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13 Solve the equation 2

6.5z 6.3z2.60 by using a graphing utility Round your answer to two decimal places

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17 If the profit from the sale of x units of a product is 2

85 400

p x  , what level(s) of x

production will yield a profit of $1100 ?

A) less than 25 units of production

B) more than 60 units of production

s  t t , where t is the number of seconds after the ball is thrown How long

after it is thrown is the height 100 feet?

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21 The time t, in seconds, that it takes a 2005 Corvette to accelerate to x mph can be

or years when the percent of total personal income used to pay personal taxes is 14percent

y x  x million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999) If the pattern indicated by the model remains valid, when

does this model predict there will be 500 million users?

A) 2001

B) 2014

C) 2011

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25 The model for body-heat loss depends on the coefficient of convection K, which

depends on wind speed v according to the equation 2

19 5

K  v where v is in miles per

hour Find the positive coefficient of convection when the wind speed is 26 mph Round your answer to the nearest integer

34

A) vertex is at a maximum point

B) vertex is at a minimum point

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29 Determine what value of x gives the optimal value of the function, and determine the

optimal (maximum or minimum) value

2

2 – 3

A) optimal value of x: 0, optimal value: 1

B) optimal value of x: –1.13 , optimal value: 0.75

C) optimal value of x: 1.50 , optimal value: –1.50

D) optimal value of x: –0.75 , optimal value: –1.13

E) optimal value of x: 0.75 , optimal value: –1.13

A) vertex: (–6, –30), a minimum point

B) vertex: (6, –42), a maximum point

C) vertex: (6, –42), a minimum point

D) vertex: (–6, –30), a maximum point

E) vertex: (–42, 6), a maximum point

Ans: A

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31 Sketch the graph of the following function

A)

B)

C)

D)

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33 Determine whether the vertex of the graph of the following function vertex is a

maximum point or a minimum point Also find the coordinates of the vertex

2

1

+ 2 – 8 0

7x xy 

A) vertex: (–7, –15), a maximum point

B) vertex: (–7, –15), a minimum point

C) vertex: (7, –15), a minimum point

D) vertex: (14, 48), a minimum point

E) vertex: (–15, 7), a maximum point

35 How is the graph of 2

yx shifted to obtain the graph of the function y(x5)2 ? 11A) shifted 5 units to the left and 11 units up

B) shifted 5 units to the right and 11 units down

C) shifted 25 units to the left and 11 units up

D) shifted 10 units to the right and 11 units down

E) shifted 5 units to the right and 11 units up

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37 Sketch the graph of the following function by using graphing calculator

A)

B)

C)

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E)

Ans: D

38 Find the average rate of change of the function between the given values of x

25

A) all values greater than or equal to 72

B) all values less than or equal to 68

C) all values greater than or equal to 10

D) all values less than or equal to 90

E) all values less than or equal to 72

Ans: E

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40 Use a graphing utility to approximate the solutions to f x ( ) 0

2( ) 3 – 20 20

A) production level of 100 units

B) production level of 10 units

C) production level of 5 units

D) production level of 50 units

E) production level of 95 units

Ans: D

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44 The daily profit from the sale of a product is given by P20 – 0.2x x2– 96 dollars What is the maximum possible profit?

46 The yield in bushels from a grove of orange trees is given by Y x1100x, where x

is the number of orange trees per acre How many trees will maximize the yield?

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49 The owner of a skating rink rents the rink for parties at $ 648 if 54 or fewer skaters attend, so that the cost per person is $12 if 54 attend For each 5 skaters above 54 , she reduces the price per skater by $0.50 Which table gives the revenue generated if

54 , 64 , and 74 skaters attend?

A) Price No of skaters Total Revenue

250

425

250

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51 In 1995, America’s 45 million Social Security recipients received a 2.6% cost-of-living increase, the second smallest increase in nearly 20 years, a reflection of lower inflation The percent increase might be described by the function

2( ) –0.4375 7.4 – 34.3625

p t  t  t , where t is the number of years past 1980 In what

year does the model predict the highest cost of living percent increase?

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52 Sketch the first quadrant portions of the following functions and estimate the market equilibrium point

2

1Supply : 10

2Demand : 84 26 5

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A) E(2.87, –4.58)

B) E(–4.58, 44.11)

( ,86)2

55 If the supply and demand functions for a commodity are given by 8p q 290 and

p2q5720, respectively, find the price that will result in market equilibrium A) 38

q p   , what is the equilibrium price and what is the corresponding number

of units supplied and demanded?

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57 The supply function for a product is 2p q 100, while the demand function for the same product is (p10)(q30)7200 Find the market equilibrium point E(q,p)

equilibrium point E(q,p) for this product when the tax is passed on (The new supply

C x   x , and the total x

revenues are given by R x( )130x Find the break-even points

A) Break-even values are at x 45 andx 65units

B) Break-even values are at x inf units

C) Break-even values are at x  inf units

D) Break-even values are at x 22.50andx 32.50units

E) Break-even values are at x 65units

Ans: A

60 If a firm has the following cost and revenue functions, find the break-even points

21

21( ) 215

A) Break-even values are at x 40 and x 160 units

B) Break-even values are at x 30 and x 110 units

C) Break-even values are at x 40 and x 110 units

D) Break-even values are at x 160 and x 110 units

E) Break-even values are at x 30 and x 160 units

Ans: E

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61 If a company has total costs 2

( ) 15, 000 35 0.1

C x   x x , and total revenues given by 2

( ) 385 0.9

R x  x x , find the break-even points

A) Break-even values are at x 300 and 175 units

B) Break-even values are at x 300 and 50 units

C) Break-even values are at x  and 427.78 units 0

D) Break-even values are at x 175units

E) Break-even values are at x 175 and 427.78 units

Ans: B

62 If total costs are C x( )1100 1500 x and total revenues are R x( ) 1620 xx2, find the break-even points

A) Break-even values are at x 10 and x 50 units

B) Break-even values are at x 10 and x 110 units

C) Break-even values are at x 50 and x 110 units

D) Break-even values are at x 10 and x 115 units

E) Break-even values are at x 50 and x 115 units

Ans: B

63 Given the profit function, P x( ) –14.5 x0.1x2300, and that production is restricted

to fewer than 75 units, find the break-even point(s)

A) Break-even value is at x 21units

B) Break-even value is at x 20.83units

C) Break-even value is at x 75units

D) Break-even value is at x 120units

E) Break-even value is at x 25units

A) Price that will maximize revenue is p $85.00

B) Price that will maximize revenue is p $191.25

C) Price that will maximize revenue is p $255.00

D) Price that will maximize revenue is p $340.00

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66 The profit function for a certain commodity is 2

P x  xx  Find the level of production that yields maximum profit, and find the maximum profit

A) Production levels of 110 yields a maximum profit of $ 900

B) Production levels of 110 yields a maximum profit of $ 2125

C) Production levels of 55 yields a maximum profit of $ 5095

D) Production levels of 55 yields a maximum profit of $ 3025

E) Production levels of 55 yields a maximum profit of $ 2125

Ans: E

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67 Use a graphing calculator to graph the profit function 2

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E)

Ans: E

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68 The graph of the profit function 2

( ) 70 0.1 6000

P x  x x  is given as follows

Consider the average rate of change of the profit from a to 350 where a lies to the left of

c Does the average rate of change of the profit get closer to 0 or farther from 0 as a gets

Ans: B

70 Suppose a company has fixed costs of $27, 600 and variable costs of 2

5 x 222 dollars

per unit, where x is the total number of units produced Suppose further that the selling

price of its product is 3

5

1275 x dollars per unit Find the break-even points

A) Break-even values are at x 1026.10 and x 26.90

B) Break-even values are at x 1053 and x  0

C) Break-even values are at x 22.48 and x 1227.52

D) Break-even values are at x 1026.10 and x 27, 600

E) Break-even values are at x 555 and x 2125.00

Ans: A

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71 Suppose a company has fixed costs of $27, 000 and variable costs of 2

5 x 222 dollars

per unit, where x is the total number of units produced Suppose further that the selling

price of its product is 3

R t  t  t , where t is the number of years past 1992 Use the

function to determine the year in which maximum revenue occurs

A) Maximum revenue occurred during 2005

B) Maximum revenue occurred during 1992

C) Maximum revenue occurred during 2004

D) Maximum revenue occurred during 2017

E) Maximum revenue occurred during 1991

Ans: C

73 Assume that sales revenues, in millions, for Continental Divide Mining can be described

by R t( ) –0.041 t20.676t0.179, where t is the number of years past 1992 Use the

function to find the maximum revenue

A) Maximum revenue is $ 8.244 million

B) Maximum revenue is $ 5.636 million

C) Maximum revenue is $ 2.786 million

D) Maximum revenue is $ 2.965 million

E) Maximum revenue is $13.996 million

Ans: D

74 Assume that costs and expenses for Continental Divide Mining can be described by

2( ) 0.011 0.526 0.722

C t   t  t and the sales revenue can be described by

2( ) 0.027 0.811 0.178

R t   t  t where t is the number of years since the beginning of

1992 Find the year in which maximum profit occurs

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75 Sketch the graph of the function f x ( ) –2

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76 Sketch the graph of the function y x+1

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77 Sketch the graph of the function y3 x–1

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78 Sketch the graph of the function below

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79 Sketch the graph of the function y x

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80

Sketch the graph of the function

2

1 if 1( )

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Harshbarger/Reynolds, Mathematical Applications for the Management, Life, and Social Sciences, 10e Ans: D

82 By recognizing shapes and features of polynomial functions, sketch the graph of the function yx3 –x Use a graphing utility to confirm your graph

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83 By recognizing shapes and features of polynomial functions, sketch the graph of the function yx2– x4 Use a graphing utility to confirm your graph

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84 By recognizing shapes and features of rational functions, sketch the graph of the function –1

– 2

x y x

 Use a graphing utility to confirm your graph

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85 Find the rational function whose graph is given

+ 1

x y x



+ 2

x y x



– 2

x y x



+ 2

x y x



– 2

x y x

Ans: D

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