EXAMPLE 4 Use an infinite series as a model Pendulums

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Presentation transcript:

EXAMPLE 4 Use an infinite series as a model Pendulums A pendulum that is released to swing freely travels 18 inches on the first swing. On each successive swing, the pendulum travels 80% of the distance of the previous swing. What is the total distance the pendulum swings?

Use an infinite series as a model EXAMPLE 4 Use an infinite series as a model SOLUTION The total distance traveled by the pendulum is: d = 18 + 18(0.8) + 18(0.8)2 + 18(0.8)3 + · · · a1 1 – r = Write formula for sum. 18 1 – 0.8 = Substitute 18 for a1 and 0.8 for r. = 90 Simplify. The pendulum travels a total distance of 90 inches, or 7.5 feet. ANSWER

Write a repeating decimal as a fraction EXAMPLE 5 Write a repeating decimal as a fraction Write 0.242424. . . as a fraction in lowest terms. 0.242424. . . = 24(0.01) + 24(0.01)2 + 24(0.01)3 + · · · a1 1 – r = Write formula for sum. 24(0.01) 1 – 0.01 = Substitute 24(0.01) for a1 and 0.01 for r. 0.24 0.99 = Simplify. 24 99 = Write as a quotient of integers. 8 33 = Reduce fraction to lowest terms. The repeating decimal 0.242424. . . is 8 33 as a fraction. ANSWER

GUIDED PRACTICE for Examples 4 and 5 5. WHAT IF? In Example 4, suppose the pendulum travels 10 inches on its first swing. What is the total distance the pendulum swings? ANSWER 50 in

GUIDED PRACTICE for Examples 4 and 5 Write the repeating decimal as a fraction in lowest terms. 6. 0.555. . . 5 9 ANSWER 7. 0.727272. . . 8 11 ANSWER 8. 0.131313. . . 13 99 ANSWER