Question

A bouncy ball is dropped such that the height of its first bounce is 6 feet and each successive bounce is 60% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).

sorry for the mess

Answer 1

Answer: 0.279936 ft or 0.3 ft rounded

Step-by-step explanation: Use an exponential function to model this equation. In this case use
`6(0.6)^(x-1)` where x represents the number of bounces. The -1 is there because it starts at 6 feet after the first bounce. Plug in 7 for x and the result is above.

Answer 2

The height of the 7th bounce of the ball is approximately 0.28 feet, rounded to the nearest tenth would be 0.3 feet.

Explanation:

To find the height of the 7th bounce of the ball, we need to calculate the height of each bounce starting from the first. We know that the first bounce has a height of 6 feet. Each subsequent bounce will be 60% of the previous bounce's height. So we can use the following formula:

height of nth bounce = 0.6^(n-1) * 6

where n is the number of the bounce we want to find the height of.

For the 7th bounce, we have:

height of 7th bounce = 0.6^(7-1) * 6

height of 7th bounce = 0.6^6 * 6

height of 7th bounce = 0.046656 * 6

height of 7th bounce ≈ 0.28 feet

So the height of the 7th bounce of the ball is approximately 0.28 feet, rounded to the nearest tenth would be 0.3 feet.