Practice B - Mathisintegral

Name———————————————————————— Lesson
4.2
Date —————————————
Practice B
For use with the lesson “Graph Exponential Decay Functions”
Tell whether the function represents exponential growth or exponential decay.
5 4 x
1. f(x) 5 ​ } ​ ​ }
​   ​  ​ 3 5
3 5 x
2. f (x) 5 ​ } ​ ​ }
​   ​  ​ 5 4
1  2
1  2
3. f (x) 5 5(2)2x
Match the function with its graph.
2 x12
4. f(x) 5 ​ }
​ 3 ​  ​
A.
B.
2
(1, 0)
C.
2
3
2
y
4
(21, 2 )
(22, 1)
x
y
4
22
1  2
1  2
y
(0, 1)
2 x21
6. f (x) 5 2​ }
​ 3 ​  ​
22
1 x
5. f (x) 5 2​ ​ } ​  ​ 1 3
2
1  2
(21, 1)
(0, 2)
x
2
x
Graph the function. State the domain and range.
1  2
y
1 x22
9. f (x) 5 3​ }
​ 4 ​  ​
11
1 x
8. f (x) 5 ​ }
​ 2 ​  ​ 2 3
1  2
1  2
y
y
2
Lesson 4.2
2
2
x
2
x
2
x
2
3 x11
11. f (x) 5 4​ }
​ 4 ​  ​
2 5
2 x
10. f(x) 5 2​ }
​ 3 ​  ​ 1 3
1  2
y
1 x24
12. f (x) 5 22​ }
​ 6 ​  ​
16
1  2
2
y
1  2
2
2
x
y
2
2
x
2
In Exercises 13–15, use the following information.
Depreciation You buy a new car for $22,500. The value of the car decreases by 25% each year.
13. Write an exponential decay model giving the car’s value V (in dollars) after t years.
14. What is the value of the car after three years?
15. In approximately how many years is the car worth $5300?
4-20
Algebra 2
Chapter Resource Book
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
1 x11
7. f(x) 5 ​ }
​ 3 ​  ​
1 2
Lesson 4.2 Graph Exponential
Decay Functions
7.
; domain: all real numbers;
range: y > 2
y
2
Teaching Guide
x
2
y increases exponentially as x increases; the value
of y decreases exponentially as x decreases.
8.
; domain: all real numbers;
range: y > 23
y
2.
2
2
1
1
y5}
​ 2 ​ (3)x; y increases as x increases; }
​ 2 ​and 2;
9.
answers
1. y 5 a(1 1 r) t where a > 0 and r > 1;
x
; domain: all real numbers;
range: y > 1
y
1
3 and ​ }2 ​ 3. Examine the value of b; b is between
0 and 1, therefore the function falls from left to
right; exponential decay
Graphing Calculator Activity
2
x
2
10.
; domain: all real numbers;
range: y < 3
y
4
1. y 5 18,000(0.88) x; $12,266.50
2
2. y 5 10,000(0.85) x; 8 yr
x
Practice Level A
1. exponential decay 2. exponential growth
11.
; domain: all real numbers;
range: y > 25
y
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
3. exponential growth 4. exponential growth
2
5. exponential decay 6. exponential growth
2
7. B 8. F 9. E 10. C 11. A 12. D
13.
y
14.
y
4
12.
2
x
2
2
; domain: all real numbers;
range: y < 6
y
x
2
x
2
15.
x
y
4
13. V 5 22,500(0.75)t 14. $9492.19 15. 5
x
2
Practice Level C
1. exponential decay 2. exponential growth
t
3. exponential growth 4. exponential decay
16. V 5 1200(0.7) ; $288.12
5. neither 6. neither
Practice Level B
7.
1. exponential decay 2. exponential growth
3. exponential decay 4. B 5. C 6. A
; domain: all real numbers;
range: y > 22
y
2
2
x
Algebra 2
Chapter Resource Book
A49