Get Ready for Grade 8 -...

Chapter 8 Patterns and Relations Chapter 8 Get Ready Chapter 8 Get Ready Question 1 Page 328 a) i) Add 3 to each term to obtain the following term. ii) Add 2 toothpicks to each term in the pattern to form one more triangle in the next term. iii) Subtract 5 from each term in the pattern to obtain the next term. b) i) The next 3 terms are 15, 18, and 21. ii) The next 3 patterns are shown. iii) The next 3 terms are 5, 0, and −5. Chapter 8 Get Ready Question 2 Page 328 Answers may vary. Sample answers are shown. a) 1 b) 2 , 7,13, ... , 4, 8, ... Chapter 8 Get Ready Question 3 Page 329 a) The next three terms are shown.

MHR • Solutions Chapter 8 429

b) c)

430 MHR • Solutions Chapter 8

d) The pattern is a straight line sloping upwards. The number of squares increases by 3 when the term number increases by 1. If I know the term number, t, I can find the number of squares, s, by multiplying by 3, and then, adding 2. e) 3 2s t= + f) To determine the number of squares in the eighth term, substitute 8 to t, and solve for s.

( )3 23 226

8s ts= +

= +

=

There are 26 squares in the eighth term.


g)


h)

hen t = 10, there are 32 squares.

hen t = 15, there are 47 squares.

hapter 8 Get Ready Question 4 Page 329

o determine the value of s when t = 25, substitute 25 for t, and solve for s.

= +

= +

=

here are 77 squares when t = 25.

hapter 8 Section 1: Explore Patterns and Relations

hapter 8 Section 1 Question 1 Page 337

)

b) The pattern is increasing by 2 squares from one term to the next.

( )3 23 10 232

s ts= +

= +

=

( )3 23 15 247

s ts= +

= +

=

W W C T

( )3 23 25 277

s ts

T C C a


Ch ioapter 8 Sect n 1 Question 2 Page 337 a)

ou sh have partial squares.

e.

Y ould not join the points with a line. You cannot b) The relation is linear. The points on the graph follow a straight lin


Chapter 8 Section 1 Question 3 Page 337 a) Multiply the term number, t, by 2, and then, add 2, to determine the number of squares, s.

) b 2 2s t= + c)

he eighth term has 18 squares, and the 25th term has 52 squares.

)

( )2 22 218

8s ts= +

= +

=

( )2 22 25 252

s ts= +

= +

=

T d 2 2

82 2 282 2 2 2 2

80 280 224

8

0

2

2

ttttt

t

= += +

− = + −=

=

=

he 40th term has 82 squares. T


Chapter 8 Section 1 Question 4 Page 337 a) Six people can be seated at the first arrangement, and 8 at the

ond arran ement.

arrangements can seat 10, 12, and 14 people.

c)

d) From the graph, you can seat 20 people at 9 tables.

sec g b) The next 3


Chapter 8 Section 1 Question 5 Page 337

y 2, a

)

a) Multiply the number of tables bcan be seated.

nd then, add 2, to determine the number of people who

2 2p t= + b c) 2 2p t= +

( )2 9 220

pp= +

=

he answer matches the answer from

d)

You can seat 62 people at 30 tables. You can check your answer using the graph if you extend the axes far enough.

T question 4, part d).

( )2 22 30 262

p tpp

= +

= +

=



) The number of toothpicks is increasing by 2 om one term to the next.

)

You should not join the points with a line. You cannot have a part of a toothpick. c) Multiply the term number by 2, and then, add 1, to obtain the number of toothpicks. d)

2 1t n= +

afr b


Chapter 8 Section 1 Question 7 Page 338 a) Substitute 6 for n, and solve for t.

( )2 12 113

6t nt == +

+

The sixth term will have 13 toothpicks.

) Substitute 75 for n, and solve for t.

2 75 1151=

he 75th term will have 151 toothpicks.

s in this pattern to have 50 toothpicks. The 2n in the of toothpicks an

=

b

2 1= + t n

( )t = +

T c) It is not possible for one of the termformula will always yield an even number, and adding 1 will make the number

dd number. o


Chapter 8 Section 1 Question 8 Page 338 a) The model is shown for 5 terms. b)


) This is not the same relation as the one in the table. The one in the table is a relation for the number of toothpicks, and increases by 2 for each term. This one is for the perimeter of the figure, and increases by 1 for each term.

2P n= + c


Chapter 8 Section 1 Question 9 Page 338 a) The plumber's earnings are increasing by $25 from one

our to the next.

)

ou should not join the points with a line. Tradesmen usually are paid for a full hour even if only part of an hour is worked.

) If you know the time worked, multiply the number of hours by 25, and then, add 35, to etermine the earnings.

d)

h b Ya cd

25 35e t= +


Chapt

) Substitute 6 for t in the equation.

= +

= +

= +=

he plumber will earn $185 in 6 h.

) Substitute 75 for t in the equation.

= +

= +

= +=

he plumber will earn $1910 in 6 h. ) Substitute $150 for e in the equation.

er 8 Section 1 Question 10 Page 338 a

( )25 3525 35150 35185

6e teee T b

( )25 3525 351875 351910

75e teee T

c

25 3525 35150

e tt

= += +

150 35 25 35 35115 2511525235

tt

t

t

− = + −=

=

=

The solution does not result in a whole number for t. The plumber cannot earn $150.



ne.

)

) The numrm to the next.

)


) Answers will vary. The 0th, 1st, and 2nd terms of a sample model are shown.

b) Answers will vary. There are many possible models for this relation. c) Answers will vary. A sample answer is shown. The prize for the winning class in a door-decorating contest is one slice of pizza for the teacher, and 3 slices of pizza for each student in the class. How does the total number of slices required relate to the number of students in the class?

a) The relation is linear. The points on the graph lie along a straight li b c ber of objects is increasing by 3 from one te d 3 4y x= + C a


Chapter 8 Section 1 Question 13 Page 339 a) Patterns will vary. A sample pattern is shown.

♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦

)

The points should not be joined. The number of objects can only have whole number values. The relation is linear. The points lie along a straight line. d) e) A short-order cook opened an 18-pack of eggs. She used 3 eggs for every breakfast order. How does the number of eggs left in the box relate to the number of breakfast orders filled?

b)

18 3y x= −

c


Chapter 8 Section 1 Question 14 Page 339 a) The o points sh uld be joined. The amount of snow can be an

) The relation is linear. The points lie along a straight line. The numbers in the table increase by 0 each time.

y real number. b2 ) The equation is c 20V t= .

200 m3 of snow will be produced in 10 h. d)

( )202 1200

00V tV=

=

=

2020

300 20t20 2015 t=

300V t

t==

=

.

he graph will become steeper. The change from one our to the next will be 40 m3 rather than 20 m3.

It will take 15 h to produce 300 m3 of snow. Assume that the rate of production remains the same ) If you double the rate of snow production, te

h



f) 20 V=

1 1010 20V = ×200=

3 of snow will be produced in 10 h.

200 m

g) 20 3001 t

t

=

will take 15 h to produce 300 m3 of snow.

15 115

= ×=

It 21 20

2 2040

r

r

=

= ×=

bli the next of 40 m3 rather than 0 m3.

Dou ng the rate of production results in a change from one hour to2

Chapter 8 Section 1 Question 15 Page 340 a) b)


c)

) For odd terms, the equation is

This is not a linear relationship. The points do not lie along a straight line. d 3 3P n= + . For even terms, the equation is

The perimeter of the 20th term will be 62 cm. The perimeter of the 50th term will be 152 cm.

3 2P n= + .

( )3 23 20 262

P nP= +

= +

=

( )3 23 50 2152

P nP= +

= +

=


e) 3 2P n= + 3 3P n


3 2100 2 3 2 2

98 398 33 3

983

100 nnnn

n

= +− = + −

=

=

=

3 3100 3 3 3 3

97 397 33 3

973

100 nnnn

n

= += +

− = + −=

=

=

either the even nor the odd equation result in a whole number for n. A term cannot have a erimeter of 100 cm.

Np

3 33 3

150 3 3 3 3147 3147 3

3 349

150P n

nnnn

n

= += +

− = + −=

=

=

3 23 2

150 2 3 2 2148 3

15

148 33 3

1 8

0

43

P nnnnn

n

= += +

− = + −=

=

=

The 49th term will have a perimeter of 150 cm.

Chap


) i) The relation is linear. The graph is a straight line.

) The relation is non-linear. The graph is not a straight ne.

ne.

iv) The relation is linear. The graph is a straight line.

ter 8 Section 2 Linear and Non-Linear Relations C a iili iii) The relation is non-linear. The graph is not a straight li


b) Situations . Sammay vary ple situations are shown. i) Sandra deposited $1000 in her bank account. Each week, she withdrew $50 to buy groceries. The horizontal axis is the time, t. The vertical axis is the amount of money left in the bank, A. ii) A skier started at the top of a hill, and skied down towards the chalet. The horizontal axis is the horizontal distance that he travelled towards the chalet, x. The vertical axis is his vertical position above the chalet, y. iii) A skateboarder performed a half-pipe. The horizontal axis is her horizontal position along the

alf-pipe, x. The vertical axis is her vertical position above the ground, y.

ss with water, placed it on his desk, but became so engrossed in a athematics problem that he forgot to drink it. The horizontal axis is the time t. The vertical axis

is the amount of water in the glass. Chapter 8 Section 2 Question 2 Page 345 a) The relation is linear. The variable x increases by a constant of 1 unit for each step, and the variable y increases by a constant of 5 units for each step.

b) The relation is non-linear. The variable x increases by a constant of 1 unit for each step, but the variable y increases by varying amounts for each step.

h iv) Charles filled a glam


Chapter 8 Section 2 Question 3 Page 345 a) The graphs are shown. b) The shapes of the graphs confirm that the first relation is linear, near.

and the second is non-li



) 10 50

50

c n

c

= +

=

100 55

001

c n

cc

= +

= +=

200 55

002

c n

cc

a) 10 50c n= + b 10 50 10 50

( )10 500 0

05

cc= +

= +( )10 5001c = + ( )10 5002c

= +

= + ( )10 5003c = +

= +=

300 55

003

c n

cc

= +

= +=

10 50


c) You shoul

he relationship is linear. The points lie along a straight line.

d not join the points. The number of people can only have whole number values.

T



) The car’s speed is increasing by 10 km/h every 5 s.

) The relationship is linear. The time values increase by a constant s from one step to the next. The speed values increase by a constant 0 km/h from one step to the next.

)

You should join the points. Both time and speed may have any real value. d) The speed limit on a major highway is usually 100 km/h. The speed should become constant at 100 km/h at a time of 25 s.

a b51 c


Chapter 8 Section 2 Question 6 Page 346 a)

b) The steps in the infested area are 2, 4, and then, 6. The next step should be 8, resulting in an area of 15 + 8 = 23 m2 after 4 weeks. The next 4 steps are 10, 12, 14, and 16, resulting in an area of 75 m2 after 8 weeks, or 2 months. c) Assumptions may vary. Assume that the pattern continues as established in the first four points.


Chapt

)

or the first five ordered pairs, the relation is linear. The points lie along a straight line.

) After 2.5 s, the parachutist is moving at 20 m/s.

) The parachutist was falling for about 4.5 s when she reached a speed of 45 m/s.

) The next 3 points do not follow the same pattern as the first five points. They are likely the peed of the parachutist after she opened her parachute.

er 8 Section 2 Question 7 Page 346 a F b c ds


Chapter 8 Section 2 Question 8 Page 346 a) Nicole

anya is 80 m closer to the finish line after the first minute, 90 m closer after the second minute, 00 m closer after the third minute, and 110 m closer after the fourth minute.

)

icole's relation is linear. The points lie along a straight line.

anya's relation is non-linear. The points do not lie along a straight line.

m the finish line, and anya was 1000 m from the finish line.

00, 200, 100, and 0. She will reach the finish line after 8 min.

Tanya's trend continues 500, 370, 230, and 80. She will still be 80 m from the finish line when Nicole reaches it.

is 100 m closer to the finish line after every minute. T1 b N T c) Nicole had a head start of 200 m. At the starting time, she was 800 m froT d) Nicole's trend continues 3


e) If the head start were by 100 m, Nicole's trend reduced would be:

900, n She would reach the finish line after 9 min. Continuing Tanya's trend, she would reach the finish line in 8.5 min. At that time Nicole will still be 50 m from the finish line. Tanya will win the race. Chapter 8 Section 2 Question 9 Page 346 Answers will vary. Sample answers are shown

he relation is likely non-linear. Sften a growth spurt when the height increases quickly. As the child approaches adulthood, the te of growth decreases, and the height becomes constant.

d 0.800, 700, 600, 500, 400, 300, 200, 100, a

. T mall children grow quickly. During the teenage years, there is ora



he creases by a constant of 1 s from one step to the next, e value of distance increases with varying values.

) The graph is shown.

he points do not lie along a traight line. The relation is non-near.

) After 2.5 s, the ski jumper avelled about 25 m down the mp.

d)

a) T relation is non-linear. Although the value of time inth b Tsli ctrra


e) The speed increases by from step to step. The rel 8 m/s ationship between speed and time is linear. f)

oth g r. The time and speed graph linear.

B raphs are increasing. The time and distance graph is non-lineais


Chapter 8 Section 2 Question 11 Page 347 a) b) The first differences are constant. This is a linear relation. c) The first differences are increasing. The second differences are constant. This is a non-linear relation.


Chapter 8 Section 2 Question 12 Page 347 Predictions will vary. a) Linear. b) Non-linear.


c) Linear.

Non-linear.

d)


e) Non-linear. f) Linear.


Chapter 8 Section 3 Slope

Question 1 Page 357 Chapter 8 Section 3

risea) slope =run2.52.51

=

=

)

b risesloperun1.55.03

10

=

=

=

c) risesloperun

=

422

=

=

risesloperun43

=

=

Chapter 8 Section 3 Question 2 Page 357 Drawings may vary.



risesloperun32

=

=


C


Chapter 8 Section 3

)

Question 5 Page 357

risesloperun632

=

=

=

a

risesloperun

441

=

−=

= −

b)

c) risesloperun6923

=

=

=


d) riseslope = run

4−623

=

= −

apter 8 Sec on 3 Question 6 Page 35

a)

Ch ti

8

risesloperun

1.82.4182434

=

−=

= −

= −

) risesloperun90

12003

40

=

=

=

b



1slope4

=a)

b)

a)

Seamis decrea b) Norm

slope 3= −


Katie and Norm are swimming in the same direction. The distance for both is increasing.

us is swimming the opposite direction. The distance for him sing.

Katie is swimming the fastest. Her graph has the steepest slope.

is swimming the slowest. His graph has the shallowest slope.




) Rodney is spending for 10 months from September to June.

He may spend a maximum of

C a

500 $5010

= per month.

Assume that he spends the same amount each month.

)

c) If Rodney spends at a faster rate, the graph slopes money before June. If Rodney spends at a slower rate, the graph slopes left at the end of June.

b

downward more steeply. He will run out of

downward less steeply. He will have money


Chapter 8 Section 3

Question 11 Page 359

a)

)

c)

b

risesloperun

1204

30

=

−=

= −

The slope indicates that the amount in the account is decreased by $30 each month.



If Sarah had to pay $35 per month, the graph would slope downward more steeply.

)

a) b The new line has a steeper slope than the original line.


c) If Sarah found a new cellular phone company that charges $25 per month, the original line ould slope downwards less steeply.

hapte

the slope is increased, the graph becomes steeper.

the slope is decreased, the graph becomes less teep.

w C r 8 Section 3 Question 13 Page 359 If Ifs


Chapter 8 Section 3 Question 14 Page 359 a) Pre

iff appears to be moving faster. His graph as a steeper slope.

)

dictions may vary. Bh

risesloperun20102

=

=

=

b

risesloperun249.52.5

=

=

The slopes indicate that Rocco is moving at bout 2 m/s, and Biff is moving at about .5 m/s. Biff is moving faster.

a2


Chapter 8 Section 3 Question 15 Page 360 a) b)

c)

risesloperun

20102

=

−=

= −

d) The slope in the table of values appears as a decrease in the distance of 2 m every second. The slope in the graph appears as a drop of 2 m for a run of 1 s. The slope in the written description appears as a speed of 2 m/s towards the door.



riserun800

12000.67

=

=

=

a) slope

occo's Run is a blue hill. R

risesloperun900

10000.9

=

=

=

iff's Breakaway is a black diamond hill. B

risesloperun1200900

1.33

=

=

=

lingshot is a double black diamond hill. S

risesloperun500

10000.5

=

=

=

enguin is a blue hill. P

risesloperun

=

=

30014000.21=

Oopsy Daisy is a green hill. b) Answers may vary. Consider obstructions such as moguls, trees and hill.

rocks when assigning a difficulty rating to a ski


Chapter 8 Section 3 Question 17 Page 360 The slope of a black diamond hill averages 0.9.

risesloperun

=

0.97500.9 750675

x

x

=

= ×=

as a rise of about 675 m.

Chapter 8 Section 3 Question 18 Page 3 Diagrams and explanations may vary. Samp The slope of a horizontal line is zero.

Sidewinder h

60

les are shown.

The slope of a vertical line is undefined. As a line approaches the vertical, its slope becomes very large.


Chapter 8 Section 4 Intersection of Two Lines on a Graph

pte 5

) Rick charges $8 for a 4-block ride, while George harges $9. Rick charges $1 less than George.

) Rick charges $12 for a 6-block ride, while George harges $11. George charges $1 less than Rick.

) Both charge $10 for a 5-block ride.

) Answers may vary.

or a ride of less than 5 blocks, select Rick. For a de of more than 5 blocks, select George.

hapte

)

b) Sally's Fitness offers the better deal up to 5 visits.

Gary's Gym offers the better deal for 7 to 10 visits.

Cha r 8 Section 4 Question 1 Page 36 ac bc c d Fri C r 8 Section 4 Question 2 Page 365 a

c) d) Both clubs offer the same deal at 6 visits.


Chapter 8 Section 4 Question 3 Page 366 a)

b) The coordinates of the intersection point are (6, 4$40.

tersection point tells you when Gary's Gym offers the

d) The part of o the right of the intersection point tells you when Sally's Fitness offers the better deal.

0). The number of visits is 6, and the cost is

c) The part of the graph to the left of the inetter deal. b

the graph t


Chapter 8 Section 4 Question 4 Page 366 a) Quick Talk charges $0.10 per minute. Chatters charges a flat $10.00 per month, plus $0.05 per

inute. b)

m


c) d) The coordinates of the intersection are (200, 200).

uihatters offers a better deal for customers who talk more than 200 minutes per month.


Quick Talk dropped their rates to 0.07 per minute, the coordinates of e intersection point would become 00, 35). The cost for 500 minutes ould be $35, the same as Chatters.

The number of minutes is 200, and the cost is $20. e) Q ck Talk offers a better deal for customers who talk less than 200 minutes per month. C C If$th(5w



we

alkalot: atterclub:

) Talkalot charges $0.08 per minute. Natterclub charges a flat rate of $12 plus $0.04 per minute.

)

Ans rs will vary. Sample answers are shown.

0.08C m= T12 0.04C m= + N

a b c) The intersection has coordinates (300, 24). Both companies charge $24 for 300 minutes.



) Timely Tools rents a power saw for $10 plus $2 per h. Rentall rents the same saw for $4 per h.

) i) of renting the power saw for t hours om each company.

) Determine the rental time that results in the same cost for each company.

) Timely Tools: ental:

oth companies charge $20 for a 5-h ntal.

Answers will vary. Sample answers are shown. a b Write relations that can be used to calculate the cost Cfr ii c 10 2C t= +

4C t= R Bre


Chapt

)

)

c) Brown: Green:

er 8 Section 4 Question 8 Page 366 a b

18 6h n= + 8 8h n= +


d) On the 25-cm shelf, Carol can arrange 2-stacks of green ots, since a 2-stack has a height of 24 cm.

n the 50-cm shelf, Carol can arrange 5-stacks of either brown en pots, since bo have a height of 48 cm.

n the 75-cm shelf, Carol can arrange brown pots, since more

p Opots or gre th Obrown pots will fit than green pots.

18 618 6

18 18 6 1857 657 66 6

9

75

.5

h nnn

nn

n

= += +

− = + −=

=

=

75

She can stack up to 9 brown pots on the 75-cm shelf.


nswers will vary.

C A



b) Donna is increasing her distance by 3 km, or 3000 m, every 20 min. Her speed is

a)

3000 150 m/min.20

=

Scott is decreasing his distance by 6 km, or 6000 m, every 20 min. His speed is 6000 300 m/min.

20=

c) The relation between distance and time is linear. Both graphs are straight lines.


d) Scott started 31.5 km, o 00 m from Newport. r 31 5 31500 210

150=

It takes Donna 210 minutes to reach Scott's starting point.

onna started in Newport. D 31500 105

300=

takes Scott 105 minutes to reach Donna's starting point.

m

t that time, Donna was 10 500 m, or 10.5 km from Newport.

It ) Froe the graph, the cyclists met after about 70 minutes.

150 70 10 500× = A


Chapter 8 Section 5 Analyse Relations Chapter 8 Section 5 Question 1 Page 373

b)

a)

risesloperun300 500

4 02004

50

=

−=

−−

=

= −

The slope means that the can is losing 50 mL of water per s. c) The slope is negative. This means that the amount of water in the can is decreasing.


Chapter 8 Section 5 Question 2 Page 373 If the ho more steeply. The amount of water in the can

ould be decreasing at a faster rate.

the hole is made smaller, the graph would decrease less steeply. The amount of water in the can ould be decreasing at a slower rate.


raphs may vary. Sample graphs are hown.

ub A has a small cross-section at the ottom,f increase of the height will be large at first, and then, ecrease.

ub B has the same cross-section at all depths. The raph will increase in a straight line.

ube C starts with a small cross-section, increases the ross-section, and then maintains a constant cross-ection. The graph will climb rapidly at first, decreasing ntil the constant cross-section is reach, and then climb t a steady rate in a straight line.


tories will vary. A sample story is shown.

illy started off towards school, remembered that he adn't picked up his lunch, and returned home. He started ff for school again, walking steadily until he reached his

When she came out, they realized that time was getting short, and they continued to the school at a much faster ace.

le is made larger, the graph would decrease w Ifw C Gs Tb but increases steadily towards the top. The rate od Tg Tcsua C S Bhofriend Cindy's house. He waited for Cindy to come out.

p



a) Matilda hiked from 0 km to 8 km, a distance of 8 km.

) The hike took 2 h. She started at t = 0 h, and finished at t = 2 h.

b

risesloperun

= c)

8 02 08

−=

−

=

the istance versus time graph.

a) b) c) The hiker who did the hike in half the time has a graph with twice the slope, or 8. The hiker who did the hike in twice the time has a graph with half of the slope, or 2.

24=

) Matilda's average speed was 4 km/h. This is the same as d

slope of the d Chapter 8 Section 5 Question 6 Page 373



)

a)

b riserun8 0.52 0

7.52

3.75

=

−=

−

=

=

slope

he speed of the hiker is 3.75 km/h.

) This speed is 0.25 km/h slower than Matilda's speed.


ce the hiker walks twice as fast, he is moving at 8 km/h.

Since he walks half as far, or 4 km, his time is

T c C Sin

4 0.58= h.


Chapter 8 Section 5 Question 9 Page 374 Rocco started 25 m from home, and moved to 15 m from

ome in 13 s, for an average speed of h 10 0.813

stopped for 3 s, and then ran the remaining 15 m in a time

m/s. He

f 4 s, for a speed of o 15 3.84

m/s.

ho

20 s, for an average speed of

Biff started 30 m from home, and ran

speed in

me at a constant

30 1.520

= m/s.

ing the race.


rary is reater than Elijah's starting distance from the

) The brothers were the same distance from home

rosses the blue line. There are two of these

er pace, not wanting to be late for dinner.

h to go by. He walked away from home, s the library, but did not see Josh. He decided to turn around before reaching the library,

nd walked home at a constant speed.

Both arrived home at the same time, ty C a) Josh's starting distance from the libgmall. The library is farther from home. b) Elijah's graph reaches a distance of 0 m before Josh's graph. Elijah arrived at home first. cat the same time at the points where the red line cpoints. d) Stories will vary. Sample stories are shown. Josh walked towards home at a constant speed. After a whifor some time. He then continued towards home at a fast Elijah stood outside the mall for a while, waiting for Jostoward

le, he met Rachel, and stopped to talk

a



b) In part A of the graph, water is flowing into the bottomsection. The height goes up slowly over time. In part B of the grap

iddle section, which has a smaller cross-section. The height goes up at a faster rate. In part C of The height goes

a)

section, which has a large cross-h, water is flowing into the

mthe graph, water is flowing into the top section, which has a small cross-section. up at an even faster rate.



risea) sloperun50 3210 0

181095

=

−=

−

=

=

he slope of the original graph is

95

T . The

lope of the reversed graph is 10 518 9

= . s

b) Points on the original graph are (0, 32),

, 41), and (10, 50).

oints on the reversed graph would be

(5

P(32, 0), (41, 5), and (50, 10).

c) riseslope = run

59

=

This matches the prediction in part a).

10 0−=

50 321018

−

=




Chapter 8 Section 5 Question 14 Page 375 Origina

a) If the initial population was 100 fish, the starting point moves to 100 on the vertical axis.

l graph.


b) If the carrying capac ty 00, the i was 5raph would level out at 500 on the

tical axis.

ecreased to 500, the graph would appear as in part b).

reats were liminated, the rate of growth would crease, and the carrying capacity would

e reached more quickly.

gver

c) If the food supply was reduced, the carrying capacity would decrease. For example, if it d d) If several disease theinb


Chapter 8 Review Chapter 8 Review Question 1 Page 376 a) As time increases by 1 s, distance increases by 3 m. b) The relation is linear. The distance changes by the same amount each second. c) Extrapolate the graph to determine that the distance after 5 s is 15 m, and after 10 s is 30 m.


Chapter 8 Review Question 2 Page 376 a) The equation for this relation is 3d t= .

)

he equation works for the ordered pairs (1, 3) and

)

he distance is 75 m after 25 s, and 180 m after 60 s.

b

( )3

133

d td=

=

=

( )9

333

d td=

=

=

T (3, 9). c

( )33 27

55

d td=

=

=

( )33 60180

d td=

=

=

T d) 3

3101000

d tt

==

00 33 3333

t

t

=

will take about 333 s to walk 1 km at this pace.

hapter 8 Review Question 3 Page 37

)

It C 6

risesloperun32

=

=

a

b) risesloperun15

0.7520

=

=

=


Chapter 8 Review Questio a) If you plan

n

to drive 20 km, the blue raph is below the red graph. Rent from oliday Rentals.

) If you plan to drive 50 km, the red raph is below the blue graph. Rent om Axle's Econo-Cars.

) The coordinates of the intersection oint are (40, 30). The rental charge is 30 for 40 km.

) If Holiday Rentals increase their ntal charge from $0.75/km to

oves to the left.

4 Page 376

gH bgfr cp$ dre$0.85/km, the slope of the graph increases, and the intersection point m


Chapter 8 Review Question 5 Page 376

) Answers

ed line:

a) b will vary. Sample answers are shown.

risesloperun2.85.01425

=

=

=

R

risesloperun

3.25.01625

=

−=

= −

Blue line:

risesloperun0

5.00

=

=

=

Green line:

c) The third line has a rise of zero, but a run that is not zero. Therefore, the slope is zero.



The number of squares in the 5th term ber of squares in the 11th term is 36. ) As the term number increases by 1, the number of squares increases by 3.

)

)

a)

b)

is 18, and the num

c

3 3s n= +

( )3 33 315 318

5s nss

= +

= +

= +=

( )13 33 333 336

1s nss

= +

= +

= +=

d e



e tap, and let the bath he turned off the tap. A short time later, she stepped

ile. Then, she ain. She pulled the

th, and let the water drain ntil the bath was empty.

hapter 8 Review Question 8 Page 377

Stories may vary. A sample is shown. Susie turned on th fill with water. Sinto the bath, and lay soaking for a whpartially sat up, and then, lay back agstopper out while in the bau C


Chapter 8 Review Question 9 Page 377 a) b) umber of cells increases by varying mounts.

)

This relation is non-linear. As the day increases by 1, the na c


Chapter 8 Practice Te t s

pter Cha 8 Practice Test Question 1 Page 378

risesloperun101001

10

=

=

=

Answer B

hapter

hapter 8 Practice Test Question 3 Page 378

elation D is non-linear. The value of y is increasing by varying mounts.

C 8 Practice Test Question 2 Page 378 C 4 8n + C Ra


Chapter 8 Practice Te t Question 4 Page 378 s

st, and then, more lowly, as the cross-section of the cone increases.

The water level increases quickly at firs Answer D


Chapter 8 Practice Te t Question 5 Page 378 s

)

)

You shoul ber. d) ying amounts. The points on the grap

a) b c

d not join the points. The number of squares must be a whole num

The relation is non-linear. The number of squares is increasing by varh do not lie along a straight line.


Chapter 8 Practice Test Question 6 Page 379

) The fixed cost is $4. Add $1 for each additional km.

)

CC= +=

The cost for a 12 km trip is $16.

a)

b

4C d= + c d) C d= +

1244

16


Chapter 8 Practice Test Question 7 Page 379

he intersection point has the (10, 80). The cost is the

ame for a 10-h rental.

or a rental of less than 10 h, Super-mps costs less.

or a rental of more than 10 h, F-Sharp Music Supplies costs less. ii) Create a table. The cost is the same for a 10-h rental. For a rental of less than 10 h, Super-Amps costs less. For a rental of more than 10 h, F-Sharp Music Supplies costs less.

i) Graph the cost versus time in hours. Tcoordinatess FA F


iii) The equation for F-Sharp Music Supplies is 6 2C t 0= + .

t+

he equation for Super-Amps is

( )6 20C = +

6 10 2080

=

= T 8C t= .

( )88 1080

C t=

=

he cos

or a rental of less than 10 h, Super-Amps costs less.

or a rental of more than 10 h, F-Sharp Music Supplies costs less.

hapter 8 Practice Test Question 8 Page 379

)

b) Both runners have covered the same distance after 300 s. c) Rajiv will finish the race first. He reaches 1500 m after 500 s, but Tommy only reaches 1500 m after 600 s.

= T t is the same for a 10-h rental. F F C a


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