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t
9. The equation for _____________ is y = C(1 – r) .
ANSWER: exponential decay
Study Guide and Review - Chapter 7
Choose the word or term that best completes
each sentence.
4
n
10. If a = b for a positive integer n, then a is a(n)
_______________ of b.
1. 7xy is an example of a(n)___________ .
ANSWER: nth root
ANSWER: monomial
Simplify each expression.
3
5
11. x ⋅ x ⋅ x
5
2. The ___________ of 95,234 is 10 .
ANSWER: ANSWER: order of magnitude
x
3. 2 is a(n) __________ of 8.
9
2 5
12. (2xy)( −3x y )
ANSWER: cube root
ANSWER: 3 6
−6x y
4. The rules for operations with exponents can be
extended to apply to expressions with a(n)
___________ such as
4
.
ANSWER: 6 6
ANSWER: rational exponent
20a b
3 2 2
14. (6x y )
n
5. A number written in is of the form a × 10 , where 1
≤ a < 10 and n is an integer.
ANSWER: 6 4
36x y
ANSWER: scientific notation
3 3 2
15. [(2r t) ]
x
ANSWER: 6. f (x) = 3 is an example of a(n) ______________ .
18 6
64r t
ANSWER: exponential function
7. 3
16. (−2u )(5u)
is a(n)
ANSWER: ______________ for the sequence
.
−10u
ANSWER: = 16 is an example of a(n)
8. 2
_______________ .
8x
ANSWER: exponential equation
9. The equation for _____________ is y = C(1 – r) .
15
3 3
18. t
10. If a = b for a positive integer n, then a is a(n)
_______________ of b.
3 3
17. (2x ) (x )
3x – 1
ANSWER: exponential decay
4
2 3
ANSWER: recursive formula
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5 2
13. (−4ab )(−5a b )
(2x )
ANSWER: 4x
9
2
19. GEOMETRY Use the formula V = πr h to find the
volume of the cylinder.
Page 1
3 3
18. (2x )
ANSWER: ANSWER: Study Guide and Review - Chapter 7
9
4x
2
19. GEOMETRY Use the formula V = πr h to find the
volume of the cylinder.
25. ANSWER: x
ANSWER: 45πx
6
26. 4
ANSWER: 1
Simplify each expression. Assume that no
denominator equals zero.
20. 27. ANSWER: ANSWER: 2 4
28. GEOMETRY The area of a rectangle is 25x y
square feet. The width of the rectangle is 5xy feet.
What is the length of the rectangle?
21. ANSWER: ANSWER: 3
5xy ft
22. Simplify.
ANSWER: 4y
29. ANSWER: 7
−3 0 6
23. a b c
ANSWER: 30. ANSWER: 3
24. 31. ANSWER: ANSWER: 5
32. 25. eSolutions Manual - Powered by Cognero
ANSWER: 6
ANSWER: Page 2
40. 0.0000543
31. ANSWER: Study
Guide and Review - Chapter 7
5
32. ANSWER: ANSWER: 5.43 × 10
−5
41. ASTRONOMY Earth has a diameter of about
8000 miles. Jupiter has a diameter of about 88,000
miles. Write in scientific notation the ratio of Earth’s
diameter to Jupiter’s diameter.
ANSWER: −2
about 9.1 × 10
33. ANSWER: 64
34. ANSWER: 4
Graph each function. Find the y-intercept, and
state the domain and range.
x
42. y = 2
ANSWER: 1; D = all real numbers;
R = {y| y > 0}
35. ANSWER: 2401
36. ANSWER: x
43. y = 3 + 1
Solve each equation.
x
37. 6 = 7776
ANSWER: 5
4x – 1
38. 4
ANSWER: 2; D = all real numbers;
R = {y| y >1}
= 32
ANSWER: Express each number in scientific notation.
39. 2,300,000
ANSWER: 6
2.3 × 10
40. 0.0000543
x
44. y = 4 + 2
ANSWER: 3; D = all real numbers;
R = {y| y > 2}
ANSWER: 5.43 × 10
−5
41. ASTRONOMY Earth has a diameter of about
of about 88,000
miles. Write in scientific notation the ratio of Earth’s
diameter to Jupiter’s diameter.
eSolutions
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miles.- Powered
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a diameter
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47. Find the final value of $2500 invested at an interest
rate of 2% compounded monthly for 10 years.
Study Guide and Review - Chapter 7
x
44. y = 4 + 2
ANSWER: 3; D = all real numbers;
R = {y| y > 2}
ANSWER: $3053.00
48. COMPUTERS Zita’s computer is depreciating at a
rate of 3% per year. She bought the computer for
$1200.
a. Write an equation to represent this situation.
b. What will the computer’s value be after 5 years?
ANSWER: t
a. 1200(1 − 0.03)
b. $1030.48
Find the next three terms in each geometric
sequence.
49. −1, 1, −1, 1, ...
ANSWER: −1, 1, −1
x
45. y = 2 − 3
ANSWER: −2; D = all real numbers;
R = {y| y > −3}
50. 3, 9, 27 ...
ANSWER: 81, 243, 729
51. 256, 128, 64, ...
ANSWER: 32, 16, 8
Write the equation for the nth term of each
geometric sequence.
52. −1, 1, −1, 1, ...
ANSWER: n−1
46. BIOLOGY The population of bacteria in a petri
dish increases according to the model p = 550(2.7)
0.008t
, where t is the number of hours and t = 0
corresponds to 1:00 P.M. Use this model to estimate
the number of bacteria in the dish at 5:00 P.M.
a n = −1(−1)
53. 3, 9, 27, ...
ANSWER: n−1
a n = 3(3)
ANSWER: about 568
54. 256, 128, 64, ...
47. Find the final value of $2500 invested at an interest
rate of 2% compounded monthly for 10 years.
ANSWER: ANSWER: $3053.00
48. COMPUTERS Zita’s computer is depreciating at a
rate of 3% per year. She bought the computer for
$1200.
a. Write an equation to represent this situation.
b. What will the computer’s value be after 5 years?
eSolutions Manual - Powered by Cognero
ANSWER: t
a. 1200(1 − 0.03)
55. SPORTS A basketball is dropped from a height of
20 feet. It bounces to
its height each bounce. Draw a graph to represent the situation.
ANSWER: Page 4
54. 256, 128, 64, ...
ANSWER: Study Guide and Review - Chapter 7
55. SPORTS A basketball is dropped from a height of
20 feet. It bounces to
its height each bounce. Draw a graph to represent the situation.
ANSWER: Find the first five terms of each sequence.
56. ANSWER: 11, 7, 3, –1, –5
57. ANSWER: 3, 12, 30, 66, 138
Write a recursive formula for each sequence.
58. 2, 7, 12, 17, ...
ANSWER: 59. 32, 16, 8, 4, ...
ANSWER: 60. 2, 5, 11, 23, ...
ANSWER: eSolutions Manual - Powered by Cognero
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