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Chapter
8
Chapter Review
8
Vocabulary Review
common ratio (p. 460)
compound interest (p. 476)
decay factor (p. 478)
exponential decay (p. 478)
Chapter Review
Resources
exponential function (p. 468)
exponential growth (p. 475)
geometric sequence (p. 460)
growth factor (p. 475)
interest period (p. 476)
scientific notation (p. 436)
Student Edition
Extra Skills and Word
Problem Practice, Ch. 8, p. 738
English/Spanish Glossary, p. 787
Properties and Formulas, p. 782
Table of Symbols, p. 779
Choose the correct term to complete each sentence.
1. The function y = a ? bx models 9 for a . 0 and b . 1. exponential growth
2. For the function y = a ? bx, where a . 0 and b . 1, b is the 9. growth factor
PHSchool.com
For: Vocabulary quiz
Web Code: atj-0851
3. Scientific notation
4. exponential decay
5. decay factor
Vocabulary and Study Skills
worksheet 8F
Spanish Vocabulary and Study
Skills worksheet 8F
Interactive Textbook Audio
Glossary
Online Vocabulary Quiz
3. 9 is a shorthand way to write very large and very small numbers. 3–5. See left.
4. The function rule y = a ? bx models 9 for a . 0 and 0 , b , 1.
5. For the function y = a ? bx, where a . 0 and 0 , b , 1, b is the 9.
6. 9 is calculated using both the principal and the interest that an account has
already earned. Compound interest
7. Each term of a geometric sequence is found by multiplying the previous term
by a fixed number called the 9. common ratio
8. The length of time over which interest is calculated is the 9. interest period
9. When a sequence has a common ratio, it is a(n) 9. geometric sequence
10. The rule y = 7x is a(n) 9. exponential function
Skills and Concepts
To simplify expressions
with zero and negative
exponents (p. 430)
To evaluate exponential
expressions (p. 432)
You can use zero and negative integers as exponents. For every nonzero number a,
a0 = 1. For every nonzero number a and any integer n, a-n = 1n.
a
Simplify each expression.
Spanish Vocabulary/Study Skills
11.
6
b-4c0d6 d4
b
22 y 8
12. x28 2
x
y
13.
14.
q4
1
2
p2q 24r 0 p
1
15. Q 25 R -4 625
16 or 39 16
16. (-2)-3 –18
17.
-2-3 –18
18.
3
7k-8h3 7h8
k
Vocabulary/Study Skills
Name
Circle the word that best completes the sentence.
1. A number in (standard form, scientific notation) is written as a product
of two factors in the form a 3 10n, where n is an integer and 1 # a , 10.
2. Each number in a sequence is called a (term, constant).
3. In a(n) (arithmetic, geometric) sequence you multiply a term in the sequence
by a fixed number.
Evaluate each expression for p ≠ 2, q ≠ –3, and r ≠ 0.
20.
p2q2 36
21.
(-p)2q-2 49
22.
pqqp 98
or
118
23.
prqr 1
4. The (Substitution, Elimination) method is a way of solving systems of
equations by replacing one variable with an equivalent expression.
5. A system of linear equations has (no solution, many solutions) when the
graphs of the equations are parallel lines.
24.
-p2q3 108
B. b c
1
C. 2a
b
6. In the function f(x) = 5x, as the values of the domain increase, the values
of the range (increase, decrease).
7. When a bank pays interest on both the principal and interest the account
has already earned, the bank is paying (simple, compound) interest.
8. A(n) (interest, growth) period is the length of time over which interest
is calculated.
25. Which expression has the greatest value for a = 4, b = -3, and c = 0? C
A. a b
L3
Date
For use with Chapter Review
Study Skill: Always read direction lines before doing any exercises. What
you think you are supposed to do with an activity may be quite different
than what the directions call for.
24 9x 2
19. 9w
4 7
x 22y 7 w y
7-2y-4 1 4
49y
Class
8D: Vocabulary
ELL
c
D. ac
b
26. Critical Thinking Is (-3b)4 = -12b4? Explain why or why not.
No; for values other than 0, (–3b)4 ≠ 81b4 u –12b4.
© Pearson Education, Inc. All rights reserved.
8-1 Objectives
9. In a relation the first set of coordinates in the ordered pairs is called
the (domain, range).
c
E. 2b
10. A base and an exponent are the two parts of a (symbol, power).
a
11. Lines in the same plane that intersect to form a 90° angle are said to
be (perpendicular, parallel).
12. The (median, mode) of a collection of data is the data item that occurs
most often.
13. The result of a single trial is called the (outcome, probability).
14. Each item in a matrix is called a(n) (term, element).
15. In the exponential function y = a ? bx, a ⬎ 0 and b ⬎ 1, the base (b)
is the (decay, growth) factor.
Chapter 8 Chapter Review
485
16. –2, 4, 12, 34, –8, 6 are examples of (real numbers, integers).
32
Reading and Math Literacy Masters
Algebra 1
485
8-2 Objectives
To write numbers in
scientific and standard
notation (p. 436)
To use scientific notation
(p. 437)
You can use scientific notation to express very large or very small numbers. A
number is in scientific notation if it is in the form a 3 10 n, where 1 # a , 10,
and n is an integer.
Is each number written in scientific notation? If not, explain.
27. 950 3 10 5
28. 72.35 3 10 8
29. 1.6 3 10-6
30. 0.84 3 10-5
No; 950 S 10.
No; 72.35 S 10.
yes
No; 0.84 R 1.
31. The space probe Voyager 2 traveled 2,793,000 miles. Write the number of miles
in scientific notation. 2.793 3 106 mi
32. There are 189 million passenger cars and trucks in use in the United States.
Write the number of passenger cars and trucks using scientific notation.
1.89 3 108 cars and trucks
8-3 and 8-4 Objectives
To multiply powers
(p. 441)
To work with scientific
notation (p. 442)
To raise a power to a
power (p. 447)
To raise a product to a
power (p. 448)
To multiply powers with the same base, add the exponents.
a m · a n = am + n
To raise a power to a power, multiply the exponents.
(am)n = a mn
To raise a product to a power, raise each factor in the product to the power.
(ab)n = a nb n
Simplify each expression.
34. A q 3r B 4 q12r 4
33. 2d 2d 3 2d 5
36. 1.342 or 1.7956
37.
243x 2y14
64
36. A 1.342 B 5(1.34)-8
35. A 5c-4 B A -4m 2c 8 B –20c4m2
37. A 12x2y-2 B 5 A 4xy-3 B -8
38. A -2r-4 B 2 A -3r 2z 8 B -1
39. Estimation Each square inch of your body has about 6.5 3 10 2 pores. Suppose
the back of your hand has an area of about 0.12 3 10 2 in.2. About how many
pores are on the back of your hand? about 7.8 3 103 pores
4
3r 10z 8
38. –
40. Open-Ended Write and solve a problem that involves multiplying exponents.
6
Answers may vary. Sample: Simplify (2a–2)–2(–3a)2; 9a
4 .
To divide powers with the same base, subtract the exponents.
8-5 Objectives
To divide powers with
the same base (p. 453)
a m = am - n
an
To raise a quotient to a power, raise the dividend and the divisor to the power.
To raise a quotient to a
power (p. 454)
a R n = an
Qb
bn
Simplify each expression.
50. Answers may vary.
Sample: Simplify and
2
use div. prop: ( a2 )–3;
use raising a quot. to a
a26
223 ;
power prop.:
use
3
the def. of neg. exp.: 26
a
8
or 6
2
41. w5 13
w
486
3
1
2
42. A 83 B · 8-5 64
43. Q 21x
3x R 7x
5 7 35
44. Q n3 R n21
v
v
26 3
3
45. e 5c c11
e
Simplify each quotient. Give your answer in scientific notation.
8
46. 4.2 3 1011
2.1 3 10
4
47. 3.1 3 10 2
12.4 3 10
3
48. 4.5 3 107
5
49. 5.1 3 10 2
9 3 10
1.7 3 10
2 3 10–3
2.5 3 101
5 3 10–5
3 3 103
8 -3
5a
50. Writing List the steps that you would use to simplify Q 6 R . See left.
a
486
w
Chapter 8 Chapter Review
10a
e
Alternative Assessment
Name
Class
You find each term of a geometric sequence by multiplying the previous term by a
fixed number called the common ratio.
To use geometric
sequences (p. 460)
To use formulas when
describing geometric
sequences (p. 461)
Give complete answers.
TASK 1
Write, solve, and graph two problems using an exponential function
(y = a ? bx). One problem should model exponential growth using
compound interest. The second problem should model exponential decay
using half-life models.
Find the common ratio in each geometric sequence.
51. 750, 75, 7.5, 0.75, c 52. 0.04, 0.12, 0.36, 1.08, c
53. 20, -10, 5, 2 52, c
0.1
3
–12
Determine whether each sequence is arithmetic, geometric, or neither. Find the
next three terms.
54. 1600, 400, 100, 25, c 55. -40, -39, -37, -34, c
25 25
geometric; 25
neither; –30, –25, –19
4 , 16 , 64
Form C
Chapter 8
TASK 2
56. 14, 21, 28, 35, c
arithmetic; 42, 49, 56
© Pearson Education, Inc. All rights reserved.
8-6 Objectives
L4
Date
Alternative Assessment
Choose a fraction and an integer to use as values for the variable m. Find the
values of m-3, m2, m-1, and m-2 ? 12.
m
You can use exponents to show repeated multiplication. An exponential function
involves repeated multiplication of an initial amount by the same positive number.
8-7 Objectives
To evaluate exponential
functions (p. 468)
Evaluate each function for the given values.
To graph exponential
functions (p. 469)
57. f(x) = 3 ? 2 x for the domain {1, 2, 3, 4} 6, 12, 24, 48
Algebra 1 Chapter 8
35
Form C Test
58. y = 10 ? (0.75) x for the domain {1, 2, 3} 7.5, 5.625, 4.21875
page 487 Chapter Review
59. a. One kind of bacteria in a laboratory culture triples in number every
30 minutes. Suppose a culture is started with 30 bacteria cells. How
many bacteria will there be after 2 hours? 2430 bacteria
b. After how many minutes will there be more than 20,000 bacteria cells?
about 180 min
69.
f (x)
6
4
2
The general form of an exponential function is y = a ? b x.
8-8 Objectives
To model exponential
growth (p. 475)
To model exponential
decay (p. 477)
67.
f (x)
60. y = 100 ? 1.025x
61. y = 32 ? 0.75 x
62. y = 0.4 ? 2x
a ≠ 100, b ≠ 1.025
a ≠ 32, b ≠ 0.75
a ≠ 0.4, b ≠ 2
Identify each function as exponential growth or exponential decay. Then identify
the growth or decay factor.
4
2
x
O
68.
2
y
63. y = 5.2 ? 3x
64. y = 0.15 ? Q 32 R
growth; 3
growth; 1.5
Graph each function. 67–68. See left.
67. f(x) = 2.5 x
2
2
When a . 0 and 0 , b , 1, the
function decreases, and the function
shows exponential decay. Then the base
of the exponent b is called the decay
factor. An example of exponential
decay is the half-life model.
O
O
70.
2
y
8
6
Identify the initial amount a and the growth or decay factor b in each
exponential function.
6
2
When a . 0 and b . 1, the function
increases, and the function shows
exponential growth. The base of the
exponent, b, is called the growth factor.
An example of exponential growth is
compound interest.
x
2
2x
x
68. y = 0.5 ? (0.5) x
65. y = 7 ? 0.32 x
66. y = 1.3 ? Q 14 R
decay; 0.32
decay; 14
69–70. See margin.
69. f(x) = Q 12 R ? 3 x
2
O
2x
x
70. y = 0.1x
71. The function y = 25 ? 0.80x models the amount y of a 25-mg dose of medicine
remaining in the bloodstream after x hours. How many milligrams of medicine
remain in the bloodstream after 5 hours? about 8.2 mg
Chapter 8 Chapter Review
487
487