Answers - MrWyatt...x4 3. 8b15 4. 3x+5 5. y3x 6. 9a2x 6.1 Practice A 1. a. 1 9 b. 27 2. a. 5 4 b. 40 3. a. 13 4 b. 11 4. exponential growth 5. exponential growth 6. exponential decay

Answers

Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A64

6.1 Cumulative Review Warm Up

1. 72 2. 4x 3. 158b

4. 53x+ 5. 3xy 6. 29 xa

6.1 Practice A

1. a. 1

9 b. 27 2. a.

5

4 b. 40

3. a. 13

4 b. 11

4. exponential growth


6. exponential decay




10. 2b = 11. 8b =

12. a. exponential growth

b. 6% increase

c. $0.25

d. 15 years

13. ( )1 0.732 ;t

y a= + growth rate 73.2%=

14. ( )1 0.223 ;t

y a= + growth rate 22.3%=

15. ( )1 0.936 ;t

y a= − decay rate 93.6%=

16. $153.32

6.1 Practice B

1. a. 1

25 b. 125 2. a.

5

2 b. 80

3. a. 26

9− b. 24


2−2

20

10

30y

x

2−2

16

8

24y

x

2−2

20

10

30y

x

2−2

4

2

6y

x

2−2

4

2

6y

x

2−2

4

2

6y

x

2−2

20

10

30y

x

Answers

Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers

A65






10. 10b = 11. 1

3b =

12. a. exponential decay

b. 20% decrease

c. $54,000

d. 2.6 yr

13. ( )1 0.0468 ;t


14. ( )61 0.016 ;y a= + growth rate 1.6%=

15. ( )1 0.996 ;t


16. $153.73

6.1 Enrichment and Extension

1. c 2. d 3. a 4. b

5. if 0a = or 1b =

6. 5xy = 7. 1

3

x

y =

8. All five functions have a y-intercept of ( )0,1 .

9. All five functions have the same domain and range; domain: all real numbers, range: 0.y >

10. a.

b. ,y x= radical function

c. domain: 0x ≥

range: 0y ≥

11. a.

b. ,y x= linear function

c. domain: all real numbers

range: all real numbers

2−2

4

2

6y

x

2−2

4

2

6y

x

2−2

4

2

6y

x

2−2

4

6y

x

2−2

20

30y

x

2−2

2

−2

y

x

642

4

2

6y

x

Answers


12. a.

b. 2 ,y x= quadratic function


range: 0y ≥

13. a.

b. 3 ,y x= cubic function


range: all real numbers

6.1 Puzzle Time

YOU TICK IT OFF

6.2 Start Thinking

semi-annual balance $7828.59,= quarterly

balance $7831.04,= monthly balance $7832.68,=

daily balance $7833.48=

Sample answer: The balance after 5 years will increase by a small amount as the number of compoundings increases. However, it seems there is a limit as to how high the balance will increase. The balance only increased by $0.80 when the number of compoundings jumped from 12 to 365.

6.2 Warm Up

1. growth; initial value 1; percent increase 20%

2. decay; initial value 1; percent decrease 22%

3. decay; initial value 1; percent decrease 37.5%


5. decay; initial value 25,000; percent decrease 5%



1. 2 10y x= +

2. 1 7

3 3y x= − +

3. 5 9y x= +

4. 3 2y x= −

5. 3 2 6y x= +

2−2

−2

2

y

x

x

y

12

20

12 20

y = 0.5x − 5

y = 2x + 10

x

y

−6

−6

y = −3x + 7y = − x +1

373

2−2

4

2

6y

x

x

y

−9

−9

y = 5x + 9

y = x − 95

x

y

−2

−2

y = (x + 2)3

y = x − 23

x

y

−2

−2

y = 2x + 63

y = x3 − 65

Answers


A67

6. 1

,2

y x= − 0x ≤

6.2 Practice A

1. 7e 2. 5e 3. 3

3

e

4. 5

5

e 5. 69 xe 6. 54 xe

7. incorrectly squared the exponent 3x, instead of multiplying by 2

( ) ( ) ( )2 223 3

6

2 2

4

x x

x

x e

e

=

=




11. ( )1 0.393 ;x

y = − 39.3%

12. ( )2 1 0.181 ;x

y = − 18.1%

13. ( )5 1 0.822 ;x

y = + 82.2%

14.

domain: ;x−∞ < < ∞ range: 0y >

15.


16.


17. a. $4415.25 b. $4376.70 c. 4.6 years

6.2 Practice B

1. 2

1

e 2.

3

3

2e 3.

12

125xe

4. 42 5 xe 5. 34 xe 6. 3 3xe +

7. incorrectly placed 42 in the denominator, although the exponent is not negative

( )4312

162 x

xe

e− =

x

y

20

10

−2 2

x

y

4

6

−2 2

x

y30

−2 2

x

y

4

2

6

−2 2

x

y

−6

4

−4 4

y = − x

y = −2x2

12

x

y

8

12

−2 2

x

y

2

−2−4 2

Answers





11. ( )1 0.284 ;x

y = + 28.4%

12. ( )3 1 0.478 ;x

y = − 47.8%

13. ( )0.25 1 1.4596 ;x

y = + 145.96%

14.


15.

domain: ;x−∞ < < ∞ range: 1y > −

16.


17. a. $5415.71 b. $5416.44

c. $4.96 d. $49.60; 10 times more


x

y

10

20

30

−2 2

x

y

4

6

−2 2

x

y

4

2

6

−2 2

x

y

4

2

6

2 4 6

x

y

8

4

2−2

Sum Approximation

2

1 112 1

3 3 5 3 − + − • •

3

1

7 3+ •

3.137852892≈

2

1 112 1

3 3 5 3 − + − • •

3 4

1 1

7 3 9 3+ − • •

3.142604746≈

2

1 112 1

3 3 5 3 − + − • •

3 4 5

1 1 1

7 3 9 3 11 3+ −

• • •)+

3.141308785≈

2

1 112 1

3 3 5 3 − + − • •

3 4 5

1 1 1

7 3 9 3 11 3+ − +

• • •

6

1

13 3•

3.141674313≈

x

y

10

4

2−2

Answers


A69

1. The number π is a mathematical constant that is the ratio of a circle’s circumference to its diameter.

2. 3.14159265359

3. The fraction 22

3.1428577

≈ is only an

approximation, just like 3.14.

4. In mathematics, a transcendental number is a number that is not the root of any nonzero polynomial. π and e are both transcendental numbers. Note that all transcendental numbers are irrational, but not all irrational numbers are transcendental. For example,

the irrational number 2 is a root of the

polynomial 2 2,x − so it is not transcendental.

5. Euler’s Identity

6.2 Puzzle Time

VACUUM CLEANER

6.3 Start Thinking

The graph of ( )1f x− is a reflection of ( )f x in the line

.y x= The domain of ( )f x is the range of ( )1f x−

and the range of ( )f x is the domain of ( )1 .f x−

6.3 Warm Up

1. 2 2. 0 3. 3

4. 1− 5. 1

2 6.

1

2−


1. a.

b.

c.

2. a.

b.

c.

6.3 Practice A

1. 32 8= 2. 17 7= 3. 25 25=

4. 4log 16 2= 5. 5log 1 0= 6. 61

log 16

= −

7. 4 8. 3 9. 1

10. 1− 11. 0 12. 3−

13. 0.699 14. 2.639 15. 0.602−

16. 30 decibels 17. x 18. 2x

19. 3x 20. 1.1logy x= 21. 3logy x=

22. 3xy = 23. ( )3 10xy =

x

y

−3

2

−2 2

x

y

2

−2

x

y

−2

2

−2−4−6

x

y

−2

2

−2 2

x

y

−2

2

−2 2

x

y

−2

2

−2 2

Answers


24. 1

3xy e= 25. 1

ln5

y x=

26. a. 208.6 mi h b. 8.2 mi

6.3 Practice B

1. 09 1= 2. 36 216=

3. 2 12

4− = 4. 13

1log 2

169= −

5. 43

log 82

= 6. 811

log 92

=

7. 2 8. 5 9. 0

10. 4− 11. 3− 12. 2−

13. 0.699− 14. 0.673 15. 2.916−

16. yes; The sound is 130 decibels.

17. 7x 18. 18 19. 3x

20. 0.75logy x= 21. 3

4

x

y =

22. ( )2 10xy = 23. 2xy e= −

24. ln 3y x= + 25. ( )6log 2y x= −

26. a. 116.83 in.; 9.74 ft

b. 1651.8 lb


1. 5 2. 3 3. 4

4. 1 5. 2 6. 1

3

7. 0 8. 2− 9. 2−

10. 343 11. 11 12. 1

216

13. 729 14. 1 15. 2

16. 1

256 17.

1

64 18.

1

3

19. 3 20. 4 21. 3

22. 512 23. 2 24. 2401

6.3 Puzzle Time

AT A SNOOPER MARKET

6.4 Start Thinking

1.

Sample answer: min 0,x = max 60,x =

scl 4,x = min 0,y = max 20,y = scl 2y =

2. approximately 6 windows after 5 days; approximately 10 windows after 10 days

3. approximately 17 windows in approximately 36 days; Note that the graph asymptotically approaches 18 from below, but never reaches it.

6.4 Warm Up

1. reflection in x-axis, followed by a translation 3 units up

2. vertical shrink by a factor of 1

,2

followed by a

translation 2 units left and 5 units down

3. reflection in y-axis, and a horizontal shrink by a

factor of 1

3

4. translation 2 units right, and a vertical stretch by a factor of 4


1. 3 5y x= + 2. 5 2y x= − −

3. 2 9y x= − + 4. 11 62

5 5y x= +

6.4 Practice A

1. translation 3 units up

00

20

60

x

y6

2

−2 2

f

g

Answers


A71

2. translation 2 units down

3. translation 1 unit right


5. horizontal shrink by a factor of 1

3

6. vertical stretch by a factor of 3

2

7. reflection in the x-axis, followed by a horizontal translation 2 units left


5 and a vertical

stretch by a factor of 2

9. incorrectly evaluates as ( )2 ,x

e but in ( ) 2 ,xf x e=

the 2 is the leading coefficient and not part of the base

10. vertical stretch by a factor of 4, followed by a translation 1 unit down

x

y

2

−3

−2 2

f

g

x

y

4

6

2

−2 2

f g

x

y

8

12

4

−2 2

f

g

x

y

8

12

4

−2 2

f

g

x

y

2

4

6

−2 2

f

g

x

y

2

2

−4

f

g

x

y

−2 2

f

g

3

1

x

y

20

30

10

−2 2 4

(1, 2e)

(2, 2e2)

(0, 2)

x

y

2 4 6

2f

g

Answers


11. reflection in the x-axis, followed by a translation 3 units up

12. ( ) 33 1xg x += − − 13. ( ) 15

4xg x e= +

14. ( ) ( )( )8log 4g x x= − +

15. ( ) ( )1 69log 2 3g x x= − −

6.4 Practice B


2. translation 2 units left




,2

followed by a

translation 1 unit down

6. reflection in the x-axis, followed by a translation 2 units left

7. translation 1 unit right, followed by a horizontal

shrink by a factor of 1

4

x

y

2 4 6

2

f

g

x

y

4

−6

−2 2

f

g

x

y

4

−2 2

fg

x

y

4

−6

−2 2f

g

f

g

x

y6

−2 2

x

y

8

12

4

2

fg

f

gx

y

2

2

−2

x

y

4

2−2

f g

Documents

Answers - MrWyatt...x4 3. 8b15 4. 3x+5 5. y3x 6. 9a2x 6.1 Practice A 1. a. 1 9 b. 27 2. a. 5 4 b. 40 3. a. 13 4 b. 11 4. exponential growth 5. exponential growth 6. exponential decay