9.08 Geometric Series Activity Worksheet Name: Title (1 point): Materials Used (1 point): Procedure (1 point): Data (30 points): Fill in the following chart: Ball 1 Description: Height 1 (starting point) Height 2 Height 3 Height 4 Height 5 Ball 2 Description: Ball 3 Description: Copy/Paste a screenshot of GeoGebra with the graphed function here. This can be done using the menu at the top of the GeoGebra screen. Go to “file,” “Export,””Graphics View to Clipboard.” Right-click in your document and choose “Paste.” (2 points) What is the graphed equation in GeoGebra. This can be found within the Algebra Window on the left. (1 point) Answer the following questions (12 points) 1. What is the common ratio between the successive height values of ball 1? Ball 2? Ball 3? 2. How does the size of the ball affect the height the ball bounces? 3. What affect, if any, does the size of the ball have on the common ratio? 4. If ball 1 were dropped from 2 feet higher, would the common ratio be different? Explain your answer. 5. What is the height of each ball on the fifth bounce (i.e. Height 6)? Use the geometric sequence formula, an = a1 r n- 1 and show your work. 6. What is the total distance of the height each ball has traveled? Use the geometric series formula: Sn = a1 – a1rn and show your work. 1–r Conclusion: (2 points) 1. What did you think of this activity? 2. What did you learn? 3. What are your strengths and weaknesses regarding exponential and logarithmic functions?

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