A bouncy ball is dropped such that the height of its first bounce is 2.5 feet and each successive bounce is 76% of the previous bounce's height. What would be the height of the 6th bounce of the ball? Round to the nearest tenth (if necessary).
To find the height of the 6th bounce of the ball, we start with the given height of the first bounce, which is 2.5 feet.
Each successive bounce is 76% of the previous bounce's height. So we need to calculate the height of each bounce, starting from the first bounce.
The height of the 2nd bounce would be 76% of the first bounce's height:
2.5 feet * 0.76 = 1.9 feet
The height of the 3rd bounce would be 76% of the second bounce's height:
1.9 feet * 0.76 = 1.44 feet
The height of the 4th bounce would be 76% of the third bounce's height:
1.44 feet * 0.76 = 1.0944 feet
The height of the 5th bounce would be 76% of the fourth bounce's height:
1.0944 feet * 0.76 = 0.830144 feet
The height of the 6th bounce would be 76% of the fifth bounce's height:
0.830144 feet * 0.76 = 0.63033984 feet
Rounding to the nearest tenth, the height of the 6th bounce would be approximately 0.6 feet.
To find the height of the 6th bounce of the ball, we can use the given information that each successive bounce is 76% of the previous bounce's height.
First, we need to find the height of the second bounce. Since the height of the first bounce is 2.5 feet, the height of the second bounce would be:
2.5 feet * 0.76 = 1.9 feet
Next, we can calculate the height of the third bounce using the same formula:
1.9 feet * 0.76 = 1.444 feet
We can continue this process to find the heights of the fourth, fifth, and sixth bounces.
Height of the fourth bounce:
1.444 feet * 0.76 = 1.0984 feet
Height of the fifth bounce:
1.0984 feet * 0.76 = 0.8344 feet
Height of the sixth bounce:
0.8344 feet * 0.76 = 0.634 feet
Therefore, the height of the 6th bounce of the ball would be approximately 0.6 feet (rounded to the nearest tenth).
after 5 more bounces, that would be
2.5 * .76^5 = ______