A bouncy ball is dropped such that the height of its first bounce is 4 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 11th bounce of the ball? Round to the nearest tenth (if necessary).

bounce 1 --- 4 ft

bounce 2 = 4(.79)
bounce 3 = 4(.79)^2
bounce 4 = 4(.79)^3
..
bounce 11 = ....

To find the height of the 11th bounce, we need to determine the height of each bounce leading up to it.

Given that the first bounce is 4 feet, we can calculate the height of subsequent bounces using the formula:

Height of nth bounce = Height of (n-1)th bounce * 0.79

So, let's calculate the heights of the first 10 bounces:

1st bounce: 4 feet
2nd bounce: 4 * 0.79 = 3.16 feet
3rd bounce: 3.16 * 0.79 = 2.49 feet
4th bounce: 2.49 * 0.79 = 1.96 feet
5th bounce: 1.96 * 0.79 = 1.55 feet
6th bounce: 1.55 * 0.79 = 1.22 feet
7th bounce: 1.22 * 0.79 = 0.96 feet
8th bounce: 0.96 * 0.79 = 0.76 feet
9th bounce: 0.76 * 0.79 = 0.60 feet
10th bounce: 0.60 * 0.79 = 0.47 feet

Now, let's calculate the height of the 11th bounce:

11th bounce: 0.47 * 0.79 = 0.37 feet

Therefore, the height of the 11th bounce is approximately 0.4 feet when rounded to the nearest tenth.

To find the height of the 11th bounce of the ball, we can use the formula:

height of nth bounce = height of (n-1)th bounce * bounce height ratio

In this case, the first bounce has a height of 4 feet and each successive bounce is 79% of the previous bounce's height.

Using the formula, we can find the height of the 2nd bounce:
height of 2nd bounce = height of 1st bounce * bounce height ratio
height of 2nd bounce = 4 * 0.79 = 3.16 feet

Similarly, we can find the heights of the 3rd, 4th, 5th, and further bounces:

height of 3rd bounce = height of 2nd bounce * bounce height ratio = 3.16 * 0.79 = 2.50 feet
height of 4th bounce = height of 3rd bounce * bounce height ratio = 2.50 * 0.79 = 1.97 feet
height of 5th bounce = height of 4th bounce * bounce height ratio = 1.97 * 0.79 = 1.55 feet
and so on...

In this case, we need to find the height of the 11th bounce. Using the same formula, we have:

height of 11th bounce = height of 10th bounce * bounce height ratio
height of 11th bounce = (height of 9th bounce * bounce height ratio) * bounce height ratio
height of 11th bounce = ((height of 8th bounce * bounce height ratio) * bounce height ratio) * bounce height ratio
height of 11th bounce = ... (continue this pattern)

Since the pattern repeats, we can use an exponentiation:
height of 11th bounce = (height of 1st bounce * bounce height ratio)^(11-1)

Plugging in the values, we get:
height of 11th bounce = (4 * 0.79)^(11-1) = (3.16)^10 ≈ 81.47 feet

Therefore, the height of the 11th bounce of the ball is approximately 81.5 feet (rounded to the nearest tenth).

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