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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. _________________________________________________________________________________________ 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. 265 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. 566