i.
To state: An infinite series to model the total distance traveled by the ball, excluding the distance traveled before the first bounce if a ball is dropped from a height of 12 feet. Each time the ball hits the ground, it bounces to 70% of its previous height.
The resultant infinite series is
Given information:
A ball is dropped from a height of 12 feet. Each time the ball hits the ground, it bounces to 70% of its previous height.
Explanation:
A ball is dropped from a height of 12 feet. It means the first term is
Each time the ball hits the ground, it bounces to 70% of its previous height. Then the common ratio will become
The nth term of geometric series is given by:
The second term is:
The third term is:
The distance will be equal to the sum of all the terms:
The distance traveled before the first bounce must be excluded. Then distance traveled will become:
Therefore, the distance traveled by the ball can be represented in a infinite series
ii.
To calculate: The total distance traveled by the ball including the distance traveled before the first bounce.
The resultant distance is 40 feet.
Given information:
The series from part (a) is
Formula used: The sum formula of an infinite geometric series with first term
Calculation:
From part (a) the total distance is:
Use the sum formula:
Therefore, the sum of the series is 40 feet. It means the total distance traveled by the ball is 40 feet.
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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