Download Using Graphs and Properties to Solve Equations with Exponents

Name ________________________________________ Date __________________ Class __________________
LESSON
15-1
Using Graphs and Properties to Solve Equations with Exponents
Practice and Problem Solving: A/B
Solve each equation without graphing.
1. 5 x = 625
________________________
1
4.
(6)x = 108
12
________________________
7.
2
(10)x = 40
5
________________________
2. 4(2)x = 128
3.
_______________________
x
6x
= 81
16
________________________
x
64
⎛4⎞
5. ⎜ ⎟ =
125
⎝5⎠
2⎛ 1⎞
1
6. ⎜ ⎟ =
3⎝2⎠
6
_______________________
________________________
x
8. (0.1)x = 0.00001
9.
_______________________
2⎛3⎞
9
=
⎜
⎟
3⎝8⎠
256
________________________
Solve each equation by graphing. Round your answer to the nearest
tenth. Write the equations of the functions you graphed first.
10. 9 x = 11
11. 12 x = 120
Equation: ___________________________
Equation: ___________________________
Equation: ___________________________
Equation: ___________________________
Solution: ___________________________
Solution: ____________________________
Solve using a graphing calculator. Round your answers to the
nearest tenth.
12. A town with a population of 600 is expected to grow at an annual rate
of 5%. Write an equation and find the number of years it is expected to
take the town to reach a population of 900.
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13. How long will it take $20,000 earning 3.5% annual interest to double in value?
_________________________________________________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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4. x = 0
MODULE 15 Exponential
Equations and Models
5. x = −1
6. x = −2
LESSON 15-1
7. x ≈ 1.1
Practice and Problem Solving: A/B
1. x = 4
2. x = 5
3. x = 4
4. x = 4
5. x = 3
6. x = 2
7. x = 2
8. x ≈ 0.8
8. x = 5
9. x = 3
10. f(x) = 11; g ( x ) = 9 x ;
9. x ≈ 6.5
x ≈ 1.1
11. f(x) = 120; g ( x ) = 12x ;
10. Not exactly. It takes about 23.4 years
at 3% and about 11.9 years at 6%. The
time at 6% is slightly more than half the
time at 3%.
11. There were 225 years from 1789 to 2014.
So, the penny would be worth
0.01(1.05)225 ≈ $585.59
x ≈ 1.9
12. 600(1.05)x = 900; 8.3 years
Practice and Problem Solving:
Modified
13. 20,000(1.035)x = 40,000; 20.1 years
Practice and Problem Solving: C
1. x = 5
1. x = 5
2. x = 3
2. x = 9
3. x = 4
3. x = 4
4. x = 3
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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