suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce. round to the nearest tenth.. my teacher told be the answers 9.2 but i don't know how she got it

Is this a geometric series? Don't you have a formula for the nth term?

no i don't

To find the height the ball rebounds to after its third bounce, we need to find the height after each bounce until the third one.

Given:

Initial height = 15 feet
Rebound percentage = 85% = 0.85

Let's calculate the height after each bounce step-by-step:

First bounce:
Height after first bounce = Initial height * Rebound percentage
Height after first bounce = 15 * 0.85
Height after first bounce = 12.75 feet

Second bounce:
Height after second bounce = Height after first bounce * Rebound percentage
Height after second bounce = 12.75 * 0.85
Height after second bounce = 10.8375 feet

Third bounce:
Height after third bounce = Height after second bounce * Rebound percentage
Height after third bounce = 10.8375 * 0.85
Height after third bounce ≈ 9.2119 feet (rounded to the nearest tenth)

So, the approximate height the ball will rebound to after its third bounce is 9.2 feet.

To determine how high the ball will rebound after its third bounce, we can use the following steps:

Step 1: Identify the initial height of the ball.
The initial height of the ball is 15 feet.

Step 2: Calculate the rebound height after the first bounce.
The ball rebounds to 85% of its previous height, so after the first bounce, the height would be:
15 feet * 0.85 = 12.75 feet

Step 3: Calculate the rebound height after the second bounce.
The previous rebound height becomes the new initial height for the second bounce. So, after the second bounce, the height would be:
12.75 feet * 0.85 = 10.8375 feet

Step 4: Calculate the rebound height after the third bounce.
Similarly, the rebound height after the second bounce becomes the new initial height for the third bounce. So, after the third bounce, the height would be:
10.8375 feet * 0.85 = 9.2119 feet

Rounding the height to the nearest tenth, we get:
9.2 feet

Therefore, according to the calculations above, the ball will rebound to approximately 9.2 feet after its third bounce.