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A rubber bouncy ball is dropped at a height of 120.00 inches onto a hard flat floor. After each bounce, the ball returns to a height that is 20\% less than the previous maximum height. What is the maximum height reached after the 7th bounce? Round your answer to the nearest hundredth.

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Answer:

To solve the problem, we need to find the maximum height reached by the ball after the 7th bounce, given that each bounce has a rebound height of 20% less than the previous maximum height.

Let's start by finding the maximum height reached by the ball on the first bounce. The ball is dropped from a height of 120.00 inches, so the maximum height reached on the first bounce is:

120.00 inches

For each subsequent bounce, the maximum height reached is 20% less than the previous maximum height. We can express this mathematically as:

maximum height = 0.8 * previous maximum height

Using this formula, we can calculate the maximum height reached on the second bounce as:

maximum height on 2nd bounce = 0.8 * 120.00 inches = 96.00 inches

On the third bounce, the maximum height reached is 20% less than 96.00 inches:

maximum height on 3rd bounce = 0.8 * 96.00 inches = 76.80 inches

We can continue this pattern for each subsequent bounce. The maximum height reached on the fourth bounce is:

maximum height on 4th bounce = 0.8 * 76.80 inches = 61.44 inches

The maximum height reached on the fifth bounce is:

maximum height on 5th bounce = 0.8 * 61.44 inches = 49.15 inches

The maximum height reached on the sixth bounce is:

maximum height on 6th bounce = 0.8 * 49.15 inches = 39.32 inches

Finally, the maximum height reached on the seventh bounce is:

maximum height on 7th bounce = 0.8 * 39.32 inches = 31.46 inches

Therefore, the maximum height reached by the ball after the 7th bounce is approximately 31.46 inches. Rounded to the nearest hundredth, this is 31.45 inches.

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