8.1 exponential properties involving products
TRANSCRIPT
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 1
8.1 Exponential Properties Involving Products
Answers
1. a. base is a
b. exponent is 5
c. the power is the exponent (5)telling us how many times to multiply βaβ
d. written as: π β π β π β π β π
2. negative
3. positive
4. negative
5. Order of operations must be applied. In the first expression you are squaring 5 first
then applying the βsign, resulting in an answer of β(5 β 5) = β25. In the second
expression because the (-5) is in brackets you keep the βsign with the 5 when you
multiply it: (β5 β β5) = 25.
6. 22
7. (β3)3
8. π¦5
9. (3π)4
10. 45
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 2
11. 3π₯3
12. (β2π)4
13. 63π₯2π¦4
14. 1
15. 0
16. 343
17. β36
18. 625
19. 177147
20. 128
21. 4096
22. 64
23. 0.00001
24. β0.216
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 3
25. 10077696
26. 4096
27. 576
28. π₯6
29. π₯9
30. π¦15
31. 6π¦5
32. 60π7
33. π12
34. π₯2π¦2
35. 81π8π12
36. β32π₯5π¦20π§10
37. 12π₯3π¦5
38. 8π₯3π¦5π§5
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 4
39. 4π6π6
40. β12800π₯5
41. 64π14
42. 1728π₯3π¦3
43. 6π₯7π¦6
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 5
8.2 Exponential Properties Involving Quotients
Answers
1. 625
2. 1296
3. 729
4. 0.003251536859
5. π
6. π₯4
7. π₯5
8. π5
9. π2π2
10. 64
11. 625
12. 10.4976
13. π3π9
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 6
14. π₯4 π¦2
15. 3π₯π¦
16. π4
16π8
17. π₯6
18. 64π2
π13
19. 3π
20. 3π₯4
21. 2.0736π24
22. 5π₯4
4π¦
23. π₯6
π¦6
24. 3.75π3
π7
25. . 44Μ π3π10
26. 3π2π4
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 7
8.3 Negative Exponents
Answers
1. π¦2
π₯
2. 1
π₯4
3. π₯4
4. 1
π₯
5. 2
π₯2
6. π₯2
π¦3
7. 3
π₯π¦
8. 3
π₯3
9. π2
π3π
10. 4π¦3
π₯
11. 2π¦3
π₯2
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 8
12. π2
π2
13. 27π6π9
π6
14. 1
15. π8
16. 5π₯β2π¦
17. 64πβ2π13
18. β27
19. 1
20. 64
21. 24
22. 9
23. 121
144
24. 512
25. 4092
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 9
26. 41
27. 36
54 or 729
625
28. 9324
29. 367
9
30. 4
35
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 10
8.4 Fractional Exponents
Answers
1. βπ23
2. π2
3. βπ₯23
π¦
4. π§7
π₯3π¦5
5. π₯βπ₯
βπ¦3
6. 27π₯3π¦β1
7. 2πβ3π2
8. 1
108π₯5π¦β5 ππ .00925926π₯5π¦β5
9. π2 πβ10
10. π₯β5π¦4
11. 3π₯π¦
12. 3π₯7π¦β2
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 11
13. πβ2πβ3π
14. π₯β1π¦
15. Β±64
16. 1
17. 49
18. 8
27 ππ .2962963
19. 1
27ππ .03703704
20. 4
21. 1
2 ππ .5
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 12
8.5 Scientific Notation
Answers
1. 310.2
2. 74000
3. 0.00175
4. 0.000029
5. 0.000000000999
6. 1.2 π₯ 105
7. 1.765244 π₯ 106
8. 6.3 π₯ 10
9. 9.654 π₯ 103
10. 6.53937 π₯ 108
11. 1.000000006 π₯ 109
12. 1.2 π₯ 10
13. 2.81 π₯ 10β3
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 13
14. 2.7 π₯ 10β8
15. 3 π₯ 10β3
16. 5.6 π₯ 10β5
17. 5.007 π₯ 10β5
18. 9.54 π₯ 10β12
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 14
8.6 Scientific Notation with a Calculator
Answers
1. 2.784 Γ 1018
2. 1.976 Γ 10β22
3. 4.59 Γ 10β5
4. 3.68 Γ 10β6
5. 1.37 Γ 1015
6. . 629Μ Μ Μ Μ Μ Μ Γ 1017
7. 1.1045 Γ 10β23
8. 7.35315 Γ 105
9. 4.17 Γ 107
10. 3.47 Γ 10β11
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 15
8.7 Exponential Growth
Answers
1. The general equation for an exponential equation is π¦ = π(π)π₯, where π is the starting
value, π is the growth factor, π₯ is the number of times the growth factor has been
applied and π¦ is the solution.
2. In a linear equation we often find a variable with an exponent, while in an exponential
growth equation the variable is always the exponent.
3. The growth factor of an exponential equation must always be greater than 1.
4. False, the form of the equation is correct, but π must be greater than 1.
5. The π¦ β πππ‘ππππππ‘ (when π₯ = 0) in any exponential growth function will always be
equal to π or the starting value, (regardless of what π is, when it is raised to the π₯
power and π₯ = 0 then ππ₯ = 1 and π times 1 is always π)
6.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 16
7.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 17
8.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 18
9.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 19
10.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 20
11.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 21
12.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 22
13.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 23
14. π¦ = π(π)π₯
π = 10 ππππππ
π = 10 ππππππ
π = 6 π€ππππ
If everyone maintains the chain then 10 million people will receive the letter the
sixth week.
15. π¦ = π(π)π₯
π = $200.00
π = 100% + 7.5% = 1.075
π = 21 β 10 = 11 π¦ππππ
By her 21st birthday Nadia will have approximately $443.12 in her account.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 24
8.8 Exponential Decay
Answers
1. Exponential decay is when a function decreases from its original value regularly
according to the noted decay factor.
2. βπβ in an exponential decay function must always be a fraction between 0 and 1.
3. If π(π₯) = π(π)π₯ then π(0) is always equal to a. (π0 will always equal 1 and π Γ 1 is π)
This means that the π¦ β πππ‘ππππππ‘ of an exponential function is always equal to π or
the starting value.
4.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 25
5.
6.
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 26
7.
8. a) Growth factor is .70.
b) Initial value is 1.
c) π(65) = 8.54 Γ 10β11
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 27
9. a.
b. π¦ = π(π)π₯ The initial value is 2,000,000 and the growth factor is ΒΎ or .75, with π₯
= time in days so: π¦ = 2,000,000(. 75)π₯
c. 10 days after β112,627
d. 14 days after β 35.636
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 28
8.9 Geometric Sequences and Exponential Functions
Answers
1. A geometric sequence is a sequence of numbers in which each number in the sequence
is found by multiplying the previous number by a fixed amount called the common
ratio.
2. a. π4 = 1 Γ 23 = 8
b. π10 = 1 Γ 29 = 512
c. π25 = 1 Γ 224 = 16777216
d. π60 = 1 Γ 259 = 576460752303000000 β 5.76 Γ 1017
3. Yes, If we divide any number by the number preceding it we always get the same
answer: -1. Therefore it is a sequence found by multiplying the previous number by a
common ratio and therefore a geometric sequence.
4. After 3 days, the population will be 81 million.
5. 6 Γ· 8 = .75, π = 0.754
6. 4 Γ· 2 = 2, π = 2
7. 3 Γ· 9 =1
3, π =
1
3
8. β8 Γ· 2 = β4, π = β4
9. 2, 6, 18, 54, 162
10. 90, β30, 10, β10
3,
10
9
11. 6, β12, 24, β48, 96
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 29
12. 192 Γ· 48 = 4, π = 4, πβπππππππ: 3, 12, 48, 192, 768
13. πβππ π =1
3, π‘βππ: 81, 27, 9, 3, 1 πβππ π = β
1
3 π‘βππ: 81, β27, 9, β3, 1
14. π =2
3, π‘βπππππππ:
9
4,
3
2, 1,
2
3,
4
9
15. π6 = 4 Γ 25 = 128
16. π4 = β7 Γ3
4
3 = 2.953125
17. π10 = β10 Γ β39 = 196830
18.
a. π¦ =. 8π₯
b. π¦ =. 85 = 0.328 ππππ‘
19.
a. 37 = 2187 blocks
b. The 6th stack is 243 blocks tall
20.
a. The ball will bounce 11.25 feet high after the third bounce.
b. The ball will bounce 0.2005 feet high after the seventeenth bounce.
21.
a. The rope will stretch 43.2 feet on the third bounce.
b. The rope will stretch 0.4354 feet on the twelfth bounce.
22.
a. After 5 hrs, or ten doublings, the population will be 30,720
b. After 12 doublings, or 6hrs, the population will be apx 123,000
Chapter 8 β Exponents and Exponential Functions Answer Key
CK-12 Basic Algebra Concepts 30
8.10 Applications of Exponential Functions
Answers
1. After six hours there will be approximately 80.8% left.
2. In the year 2020 there will be approximately 1147 bird species left.
3. In the year 2007 there would be approximately 370 stores in Nadiaβs chain.
4. In 12 years there will be approximately $833.82 in the account.
5. Approximately 120,481
6. About 3840 bacteria
7. Approximately $13.44, 5 years from now.
8. a.
b. π¦ = 7200 β 0.82π₯
c. $989.63
9. a. π¦ = 10,112,620 β 0.995π₯
b. 9,715,124
c. About 4.25 years (early in 2008)
d. 10,317,426