Solution manual for applied CALC 2nd edition by wilson

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2 Temperature is a function of the time

of day since at any time of the day when the temperature is measured, the measured temperature will be a single value

3 The input value 182 has two different output values (32 and 47)

Therefore, the number of salmon in a catch is not a function of the number

of fish caught

4

The total cost of four pairs of shoes

6 p 12 3.55

On June 16, 2012 (12 days after June

4, 2012), the average retail gas price was $3.55/gallon

at that point would touch the graph

in multiple locations However, if the graph doesn’t actually go vertical nearx1, then it is the graph of a function One drawback of reading a graph is that it is sometimes difficult

to tell whether the graph goes vertical or not

9 The graph represents a function since any vertical line drawn will touch the graph exactly once

10 The graph represents a function since any vertical line drawn will touch the graph exactly once

11 y      x2 4; 3 x 3, 10 y 1

12 y 2x2      1; 2 x 2, 3 y 2

13 y5 x x2; x1From the graph, it appears that y4

at x1 We calculate the exact

value of y algebraically

 4 39.95 4 159.80



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2 CHAPTER 1 Functions and Models

 2

5 1 1

5 14



 

From the graph, it appears that y2

at x 2 We calculate the exact

But division by zero is not a legal

operation Therefore, the function is

not defined when x 2

Graphically speaking, there is a

“hole” in the graph at x 2

15 The function f p( ) p22p1 has

the domain of all real numbers

domain of all real numbers since no

value of r will make the denominator

1 01

a a

 

 

The denominator is always positive

The domain of the function is the set

of all real numbers greater than or equal to –3 That is, x x|  3

20 Since it doesn’t make sense to sell a

negative number of bags of candy, n

is nonnegative The domain of the candy profit function is the set of whole numbers That is,

n n| is a whole number

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   

0.23.4 0.2 1.2 substituting 1.2, 3.43.4 0.24

3.64

y mx b

b b b

1 The constant rate of change (slope)

of the line passing through (2, 5) and (4, 3) is

3 5

4 2221

of the line passing through (1.2, 3.4) and (2.7, 3.1) is

3.1 3.42.7 1.20.31.50.2

of the line passing through (2, 2) and (5, 2) is

2 2

5 2030

x x x

y y

x x x

y mx b

b b

  



The slope-intercept form of the line

is y  x 7 The standard form of the line isx y 7 A point-slope form of the line is y  5 1x2

8 The slope of the line passing through (1.2, 3.4) and (2.7, 3.1) is

3.1 3.42.7 1.20.31.50.2

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is y 0.2x3.64 The standard

form of the line is typically written

with integer coefficients Therefore,

is the standard form of the line

A point-slope form of the line is

m 

 



Since the slope is equal to zero, this

line is a horizontal line The

slope-intercept form of the line is

0 2

y x and is commonly written

as y2 The standard form of the

line is 0x y 2 and is also often

written as y2 A point-slope form







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3

y x

15 This is a vertical line with x-intercept

 3, 0 The equation of the line is 3

x

16 If the package weight increases from

1 pound to 2 pounds, the cost increases $(7.95 – 5.51) = $2.44

But if the package weight increases from 2 pounds to 3 pounds, the cost increases $(10.20 – 7.95) = $2.25

Since the rate of change (rate of price increase, or slope) is not constant, the table of data may not be represented by a linear function

17 As letter weight increases from 4 to

5 ounces, the cost increases $(1.70 – 1.50) = $0.20 Similarly, as letter weight increases from 5 to 6 ounces,

6 to 7 ounces, and 7 to 8 ounces, the cost increases $0.20 each time The rate of change (rate of price increase,

or slope) is constant, so the table of data may be represented by a linear function The constant rate,

$0.20/ounce, indicates that for each additional ounce of weight in a standard-sized letter shipped from Queen Creek, Arizona to Ellensburg, Washington, the cost will increase

$0.20

18 If the table of data represents a linear

function then a linear function passing through two of the points will also pass through all other points

in the table

Clean Wood (Pounds)

Cost to Dispose

of Clean Wood

at Enumclaw Transfer Station

00.0375

b b

y y

These results match the table data

The data table may be represented by

a linear function It costs an average

of $0.0375 per pound to dispose of clean wood

19 Let x be the number of servings of

WheatiesTM and y be the grams of

fiber consumed We have

2.1 3.3

y x

since each serving of cereal contains 2.1 grams of fiber and the banana

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contains 3.3 grams of fiber We must

solve

8 2.1 3.34.7 2.12.2383

x x x





In order to consume 8-grams of

fiber, you would need to eat 3

servings ( 1

4

2 cups) of Wheaties along with the large banana

20 The slope of the line is

 

4 490undefined

Therefore, the line is a vertical line

Although the y-values change, every

point on a vertical line has the same

-value

x The x-value of each of the

points isx4 The equation of the

vertical line is x4

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 0 7

ya x x since  0, 0 and

 7, 0 are x-intercepts of the

function Substituting 2,10 into this equation yields

  

10 2 0 2 7

10 2 51

a a a

b a and substituting 2 a for b

in the second equation yields

8 The graph appears to pass through

0, 3  and have vertex 2,1 Each of these points will satisfy 2

224

b a

a a

 

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Since b4 ,a b 4 The graph’s

equation is 2

4 3

y  x x

9 The graph appears to pass through

 0,5 and have vertex 5, 20  

Each of these points will satisfy

2

yax bx c Since the

y-intercept is  0,5 ,c5 Since the

x-coordinate of the vertex is

2

b x a

5210

b a

Substituting the coordinates5, 20 

into the equation yields

Substituting the coordinates of the

other two points into the equation

a a

The second differences are constant,

so the data represent a quadratic function

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16 The parameter a is 0.05 and

represents that the rate at which the change in the number of members of the USAA per year is increasing is 0.10 million people per year The

parameter b is 0.15 and represents

the increase in the number of members of the USAA per year in the initial year of 2003 The

parameter c is 5.0 million and

represents the number of members of the USAA in the initial year of 2003

17 The parameter a is -19.56 and

represents that the rate at which the population of the United States per year is changing is decreasing 39.12 thousand people per year The

parameter b is 3407 and represents

the increase in the number of thousand people in the United States

per year in the initial year of 1990

The parameter c is 250,100 and

represents the number of thousand people in the United States in 1990

represents that the rate at which the change in the number of students enrolled in the Arizona Virtual Academy is increasing is 282.5 students per year each year The parameter b is 358.75 and represents the increase in the number of

students enrolled in the Arizona Virtual Academy in the initial year

of 2003 The parameter c is 318.75

and represents the number of students enrolled in the Arizona Virtual Academy in the year 2003

19 The parameter a is -31.15 and

represents that the rate at which the change in the amount of money spent

by consumers on books classified as adult trade is decreasing is 62.30 million dollars per year each year

The parameter b is 556.1 and

represents the increase in the amount

of money in millions spent by consumers on books classified as adult trade in the initial year of 2004

The parameter c is 14970 and

represents the amount of money in millions spent by consumers on adult trade books in the year 2004

represents that the rate at which the change in the amount of yogurt produced in millions of pounds is increasing is 29.98 million pounds

per year each year The parameter b

is 62.14 and represents the increase

in yogurt production in millions of pounds per year in the initial year of

1997 The parameter c is 1555 and

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represents the millions of pounds of

The vertical intercept is found by

substituting 0 for x The vertical

intercept is  0,5

24 For the vertex,

2002(9)

b x a x

y y

 

The vertex is 0, 4  The vertical intercept is found by

intercept is 0, 4   (The vertical intercept is the vertex in this case.)

25 For the vertex,

2

b x a

intercept is  0,1

26 We substitute 150 for j t in the  

given function rule and solve for t:

2 2 2

150 0.0990 1.28 154

1.28 1.28 4 0.0990 4

2 0.09901.28 1.7951040.198

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27 We substitute 650 for j t in the  

given function rule and solve for t:

2 2

(corresponding to t3.64 years after 1998) and 2016 (corresponding

to t18.23 years after 1998)

28 We maximize the quadratic function

at the vertex of its graph To find the first coordinate of the vertex, we compute

21.020.082212.40876

b t a t t

29 a We compute the x-coordinate of

the vertex of the graph of r x  

to determine the number (of millions, it seems, judging from part (b)) of iPads that need to be sold to maximize revenue

2703

2 6.7352.2288

b x a

b Given that 52.2 million is considerably higher than 15.4 million, it may not be reasonable that Apple will maximize

quarterly iPad sales revenue

30 We compute the x-coordinate of the

vertex of the given quadratic profit function:

2267

2 304.45

b x a

The number of items ordered (sold)

is given by the expression 10x1

Computing 10 4.45 1 gives 45.5

If 45 items are sold, then x4.4,and the profit is P 4.4 621dollars If 46 items are sold, then 4.5,

x and the profit is

 4.5 621

P  dollars Thus profit is maximized at $621 when 45 or 46 items are sold

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Exercises 1-4

1 f x is cubic because the third  

differences are constant

x f(x) 1st diffs 2nd diffs 3rd diffs

g x is linear because the first

differences are constant

h x is none of these because none

of the first, second, or third differences are constant

x h(x) 1st diffs 2nd diffs 3rd diffs -5 11.2

g x is quadratic because the

second differences are constant

h x is none of these because none

of the first, second, or third differences are constant

x h(x) 1st diffs 2nd diffs 3rd diffs

Solution Manual for Applied CALC 2nd Edition by Wilson

Full file at https://TestbankDirect.eu/Solution-Manual-for-Applied-CALC-2nd-Edition-by-Wilson

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1-4 Polynomial and Rational Functions 13

3 The concavity changes one time so the type of polynomial function represented by the graph is a cubic function

4 The concavity changes three times so the lowest degree polynomial

function that could represent the graph is a fifth degree polynomial

5 The concavity changes two times so the lowest degree polynomial function that could represent the graph is a fourth degree polynomial

6 The concavity changes one time so the lowest degree polynomial function that could represent the graph is a third degree polynomial

100,000 5 x 1091,000,000 5 x 1011

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18 horizontal asymptote: ( )k x 0; vertical asymptote is 3

2

x  (Note that x1is NOT an asymptote but rather a hole.)

19 no hole exists vertical asymptote: x3 horizontal asymptote: y2vertical intercept: 1

3(0)

f   or 1

3(0, )horizontal intercept: (set numerator =

2

x  or 1

2( , 0)

20 no hole exists vertical asymptote: 1

horizontal intercept:(set numerator = 0) 4

3

x or  4

3, 0

2 2

Full file at https://TestbankDirect.eu/Solution-Manual-for-Applied-CALC-2nd-Edition-by-Wilson Full file at https://TestbankDirect.eu/Solution-Manual-for-Applied-CALC-2nd-Edition-by-Wilson

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1-4 Polynomial and Rational Functions 15

2 2

8(0)

f   or 3

8(0, )horizontal intercepts: (set numerator = 0)

2 and 1

x x  or (2, 0) and ( 1, 0)

22

no hole exists vertical asymptote:

5 and 22

horizontal intercepts: (set numerator

2 2

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24 a B w h( , ) 7052w

h

 , w 190 pounds,

705(190) 133,950(190, )

25 a

6000.08

200(169 0.6 )16(169 0.6 ) 600

2704 590.44.56

n n

110(169 0.6 )8.8(169 0.6 ) 600

1487.2 594.722.5

n n

d As t , ( )r t 0 This means that if the patient takes

“forever” to complete the workout, then the pace of the

workout is really slow

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1-5 Exponential Functions and Logarithms 17

0 1 2 3 4

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6 The y-intercept is  0, 2 so a2

We have 6

2 3

b  The exponential function is y2 3 x We will check our result by evaluating the function

We will determine the value of a by

plugging in the point 1,10 

x

y a a a a

1 4 1 2

41614

4464

a a a

We will determine the value of a by

plugging in the point  1,1

 1

1 40.25

a a a



Therefore, y0.25 4 x We will check our solution with the point

1

5 0

1 5

825613212

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