A ball is dropped from a height of 256 ft. With each bounce, the ball reaches a height that is half the height of the previous bounce. After which bounce will the ball rebound to a maximum height of 1 ft?

y.2^x=256

y = 1 ft
==> x= log_2_(256) = 8

To determine the number of bounces until the ball reaches a maximum height of 1 ft, we need to understand the pattern of heights during the bounces.

Given that the initial drop height is 256 ft, each subsequent bounce reaches a height that is half of the previous bounce. Let's list the heights for the first few bounces:

Bounce 1: 256 ft
Bounce 2: 256 ft / 2 = 128 ft
Bounce 3: 128 ft / 2 = 64 ft
Bounce 4: 64 ft / 2 = 32 ft
Bounce 5: 32 ft / 2 = 16 ft
Bounce 6: 16 ft / 2 = 8 ft
Bounce 7: 8 ft / 2 = 4 ft
Bounce 8: 4 ft / 2 = 2 ft
Bounce 9: 2 ft / 2 = 1 ft

From the sequence of bounces, we can observe that the ball reaches a maximum height of 1 ft after the 9th bounce.

Therefore, the ball will rebound to a maximum height of 1 ft after the 9th bounce.