Name ________________________________________ Date ___________________ Class __________________
LESSON
12-2
Reading Strategies
Analyzing Information
An exponential function is always in the form f (x) abx. And the graph of an exponential
function is always the same general shape. But the values of a and b determine the quadrants
the graph is in, and the “direction” in which the graph is facing. Analyze the information in the
examples below.
y
2(3)x
y
a!0
b!1
2(3)x
a0
b1
y abx
a0
0b1
a!0
0b1
y
§ 1·
2¨
© 3 ¹̧
x
y
§ 1·
2¨
© 3 ¹̧
x
Respond to each statement by writing sometimes, always, or never.
1. When a is negative, the graph of
y abx is contained entirely in quadrants
III and IV.
2. When b is a fraction, the graph of
y abx is contained entirely in
quadrants I and II.
_____________________________________
3. The y-intercept of y
_____________________________________
x
ab is at a.
4. The graph of y
_____________________________________
abx is a straight line.
_____________________________________
5. Complete the table of values and
sketch the graph of y 3(2)x.
x
y
1
0
1
2
© Houghton Mifflin Harcourt Publishing Company
296
Holt McDougal Coordinate Algebra
2.
The bases are reciprocals.
The graphs are reflections across the
y-axis.
8.
x
y
1(2)x
1
y
1
y
1(2)
0
y
1(2)0
1
1
y
1(2)
1
2
2
y
1(2)2
4
3. The bases are reciprocals of one another
and the graphs are reflections of one
another across the y-axis.
1
4. Because 10 and
are reciprocals
10
1
§ 1·
5. Because 0.2 ¨ ¸ and 5 and
5
5
© ¹
0.5
are reciprocals
x
6. Because 4
1
§ 1·
¨ 4 ¸ and 4 and 4 are
© ¹
x
reciprocals
7. Because 1.25
and
x
§5·
¨4¸
© ¹
x
x
5
§4·
¨ 5 ¸ and 4
© ¹
4
are reciprocals
5
Problem Solving
1. a. 30.375 in.
Challenge
b.
2. 4 years; 32 years
1.
3. $202.41
4. 2210
5. B
6. C
7. J
Reading Strategies
1. always
2. sometimes
3. always
4. never
The bases are reciprocals.
The graphs are reflections across the
y-axis.
© Houghton Mifflin Harcourt Publishing Company
A66
Holt McDougal Coordinate Algebra
5.
4. y
50,000(1.0025)12t; |$59,847.42
x
y
5. y
43,000(1.05)t; |$49,777.88
1
3
2
6. y
65,000(1.015)4t; |$132,826.09
7. y
2500(0.97)x; |2147
0
3
8. y
25,000(0.85)x; |$6812.26
1
6
9. 2.1875 grams
2
12
Practice C
1. y
375,000(1.0675)x; |$675,059.76
2. y
273,000,000(1.006)x; |286,382,511
3. y
30,098(1.036)x; |$39,940.70
4. y
60,000(1.025)t; |$73,104.17
5. y
27,000(1.009375)4t; |$30,199.12
6. y
95,000(1.0035)12t; |$144,480.36
7. y
1800(0.962)x; |1427
8. y
2300(0.989)x; |$2129
9. |0.117 grams
12-3 EXPONENTIAL GROWTH AND
Review for Mastery
DECAY
Practice A
1. y
372,000(1 0.05)t; |$549,613
2. y
4200(1.03)t; |5165
3. y
350,000(1 0.03)t; |$291,540
1. y
270,000(1 0.07)t; y
2. y
2200(1 0.02)t; y | 2478
4. y
1200(0.98)t; |1085
3. y
200(1 0.08)t; y | $503.63
5. A
17,000(1.03)t; $20,298.89
4. A
§
0.03 ·
20,000 ¨ 1 1 ¹̧
©
6. A
0.02 ·
§
23,000 ¨ 1 ; $26,979.99
4 ¸¹
©
$330,761.61
4t
(1)(t )
;
A | $25,335.40
7. A = 30(0.5)t; 3.75 g
§
0.06 ·
35,000 ¨ 1 12 ¹̧
©
A | $63,678.89
(12)(t )
5. A
8. A = 40(0.5)t; 2.5 g
Challenge
;
1. A
10,000(1.0565)t
2.
4t
6. A
0
1
2
3
t
A 10,000 10,565 11,161.92 11,792.57
7. y
800(1 0.02)t; y | 738
4
5
6
7
12,458.85 13,162.78 13,906.47 14,692.19
8. y
2300(1 0.04)t; y | 1529
9. A
10(0.5)t; A
§
0.08 ·
35,000 ¨ 1 ;
4 ¹̧
©
A | $52,008.16
3. a. sometime after the end of the
third year but before the end of the
fourth year
2.5 grams
Practice B
1. y
650,000(1.04)x; |$790,824.39
2. y
800(1.02)x; |901
3. y
70(1.18)x; |136
b. sometime after the end of the
third year but before the end of the
seventh year
4. 7.4 years
© Houghton Mifflin Harcourt Publishing Company
A67
Holt McDougal Coordinate Algebra