Let's first convert the maximum height of 25 cm to meters:
25 cm = 0.25 m
Let's represent the number of bounces as "n". We know that with each bounce, the ball reaches a height that is half the height of the previous bounce. Therefore, the height of the nth bounce can be represented as:
32 x (1/2)^n
We want to find the bounce where the ball rebounds to a maximum height of 0.25 m. So we can set up an equation:
32 x (1/2)^n = 0.25
Simplifying this equation, we get:
(1/2)^n = 0.25/32
(1/2)^n = 0.0078125
Taking the logarithm of both sides with base 0.5, we get:
n = log0.5(0.0078125)
n = 7.0
Therefore, the ball will rebound to a maximum height of 25 cm after 7 bounces.