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MATH 153
PRECALCULUS
UNIT 2 HOMEWORK ASSIGNMENTS
General Instructions
- Be sure to write out all your work, because method is as important as getting the correct answer.
- The answers to the odd-numbered problems are in the back of the book, beginning on page 641. The answers to the even-numbered problems and to the “Additional Problems” are at the end of this handout.
- Note that some of the problems that have been assigned are review problems from previously covered sections. These will help you to prepare for the tests because the tests are cumulative.
Chapter 7
Section 7.1 – Introduction to the Family of Exponential Functions
A.Text: Appendix A, page 566:5, 6, 15, 17, 21, 24, 29, 31, 33
Page 396:1 – 9 odd, 13, 14, 15, 16, 17, 19, 20, 25
Page 303: 10, 11
B.Additional Problems:
1.Are the functions the same or different? Explain.
Section 7.2 – Comparing Exponential and Linear Functions
A.Text: Page 403:1, 2, 3, 4, 5, 6, 11, 12, 17, 19, 23, 25, 26, 29, 37, 39
Page 309: 2, 7
B. Additional Problems:
1.For the functions in a) and b), find the average rate of change between the points
(i) and
(ii) and
(iii) and
a)b)
Section 7.3 – Graphs of Exponential Functions
A. Text:Page 410: 1 – 7 all, 9, 10, 13, 15, 16, 20, 21, 25, 27, 30, 31, 34, 37
Appendix A, page 566: 36, 40, 44, 45, 48, 52, 63, 65, 66
Page 309: 16, 25
Section 7.4 – Continuous Growth and the Number e
- Text:Page 418:1, 2, 3, 5, 11, 13, 14, 15, 17, 20
B. Additional Problem
1. Solve the inequality. Express your answer in interval notation.
Section 7.5 – Transformations of Exponential Functions
A.Text:Page 430:1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19
Page 77: 17
Page 86: 2, 3, 11 – 17 odd, 23
Page 412: 28
Page 328: 5, 23
Appendix A, page 566: 67, 74, 78, 79, 87 – 95 odd.
B. Additional Problem:
1.Solve these equations by writing both sides with the same base and then using the property below.
Property: If , then .
a.b.c.
d. = 1000e. f.
Chapter 8
Section 8.1 – Logarithms and Their Properties
A.Additional Problems
1.Write each equation in exponential form:
a.b. c.
d.e. f.
2.Write each equation in logarithmic form.
a. b. c.
d. e. f.
3.Solve for x by writing each equation in exponential form.
a. b. c.
4.Solve the equation. Give an exact solution and a four decimal place approximation.
5.Simplify the left side of each equation using properties of logarithms, then solve exactly.
a.b.
6.Use the change of base formula and a calculator to evaluate each expression. Round your answer to six decimal places.
a. b. c.
B.Text:Page 445:1, 3, 7, 8, 11, 13, 15, 20 – 27 all, 29, 33 – 37 odd, 38, 39, 45, 47
Section 8.2 – The Logarithmic and the Exponential Models
A. Text:Page 453:1 – 15 odd, 19, 24, 27, 29, 31, 36, 37 (in part (c), solve algebraically,
check graphically), 45
Page 338:10, 12, 14
Section 8.3 – The Logarithmic Function
A.Additional Problems
1.Write the definition of a logarithmic function.
2.Draw the graph of a logarithmic function with base >1. What point do all such graphs have in common?
B.Text:Page 461: 1, 2, 3 – 9 odds, 27, 29
C.More Additional Problems
1.Find the domain of each function algebraically.
a)b)
Section 8.4 – Transformations of Logarithmic Functions
A.Text:Page 469:1, 2, 3 – 9 odd
Page 453: 11, 12
Page 79: 35
Page 86: 25
B.Additional Problems
For each quadratic function, find all intercepts and the vertex without using a calculator. Then sketch a graph of the function.
1)2)
Section 8.5 – Comparing Power, Exponential and Log Functions
A.Text Page 473:1, 2, 4, 5, 6, 8, 9, 11, 17, 19, 21, 23, 25, 27
B.Additional Problems
1.Without using your calculator, match the following graphs on the next pagea – l with their possible equations 1 – 20. Some equations will not be used.
2.
3.
a. / b. / c.d. / e. / f.
g. / h. / i.
j. / k. / l.
1. / 2. / 3. / 4.
5. / 6. / 7. / 8.
9. / 10. / 11. / 12.
13. / 14. / 15. / 16.
17. / 18. / 19. / 20.
1
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Answer Key
7.1
Appendix A, p. 566
5.1
6.–1
15.16
17.
21.
24.
29.
31.
33.2
p. 396
14.411.8 items
16.a. Towns (i), (ii), and (iv) are growing. Towns (iii), (v), and (vi) are shrinking.
b. Town (iv) grows fastest, at 18.5% per year.
c. Town (v) shrinks fastest, at 22% per year.
d. Town (iii) has the largest initial population, at 2500.
Town (ii) has the smallest initial population, at 600.
20.a.
b. $14.92
p. 303
10.
B.Additional Problems
1. are different.
is a quadratic function; the base is variable and the exponent is a constant. is an exponential function; the base is a constant and the exponent is variable.
7.2, p. 403
2.a.
b.
c.
4.Exponential function because it grows by a constant percentage.
6.a. exponential
b.
12.
26.
p. 309
2. x-intercepts:
y-intercept:
horizontal asymptote:
vertical asymptote: none
B.Additional Problems
1. a)(i) 2
(ii) 2
(iii) 2
b)(i) 2
(ii) b + a
(iii)
7.3, p. 410
2. A and B
4.A
6.
10.
16.a.
b.
.
Window:
Window:
c. 23.362 years
20.a. all are positive
b. b
c. a, b, c, p
d. a = c
e. d and q
30.The friend entered . This is a linear function.
34.Domain: all numbers
Range:
Appendix A, page 566
36.8
40.
44.
45.49
48.–121
52.–5
63.
65.
66.
p. 309
16.(a) (iii)
(b) (i)
(c) (ii)
(d) (iv)
(e) (vi)
(f) (v)
7.4, p. 418
2.(a) III, (b) II, (c) IV, (d) I
14.
20. a. $1270.24
b. $1271.01
c. $1271.22
d. $1271.25
B.Additional Problem
1.
7.5, p. 430
2.g(x) is a vertical stretch by a factor of 2.
h(x) is a horizontal squeeze by a factor of 2.
p. 86
2.. Reflection about the y-axis.
p. 412
28.
Horizontal asymptote
Appendix A, page 566
67.
74.3a
78.–8
79.–8
87.False
89.True
91.False
93.True
95.False
B.Additional Problem:
1. a., , x = 3
b.
c.
x = 0
d.=
x = –3
e.
1 – x = –1
x = 2
f.
8.1 Additional Problems
1.a.
b.
c.
d.
e.
f.
2.a.
b.
c.
d.
e.
f.
3.a.
b.
c.
4.
5. a.
b.
6.a.
b.
c.
p. 445
8.
20.a. 0
b. –1
c. 0
d.
e. 5
f. 2
g.
h. 100
i. 1
j. 0.01
22.a. 0
b.
c.
d. 27
e.
f. 1
24.a. 2x
b. 3x + 2
c. –5x
d.
26.a. False
b. True
c. False
d. False
38.
8.2, p. 453
24.
36. a. , t in hours
b. About 30.1 hours
p. 338
10.
12.
14.
8.3, Additional Problems
1.A logarithmic function is a function of the form , where x > 0 and .
2.
The common point is (1, 0).
p. 461
2.
C. More Additional Problems
1. a., so
b.
8.4, p. 469
2. i)
ii)
iii)
iv) decreasing
v)
vi)
p. 453
12.
B. Additional Problems
1.
2.
8.5, p. 473
2.(i)A
(ii)C
(iii)D
(iv) B
4. (i)D
(ii)B
(iii)A
(iv) C
6.
8.
B. Additional Problems
1.
a.17
b.14
c.18
d.5
e.10
f.1
g.12
h.15
i.2
j.3
k.13
l.7
2.
3.
1