Brady dropped a bouncy ball from a height of 64 feet. After the second bounce, the ball reached a height of 36 feet. write a rule to represent the height of the ball after each bounce, then find the height after the fourth bounce

Height = 20.248 ft

Step-by-step explanation:

We can model this process with an exponential function

Height = Initial_Height * (e) ^ (k*x)

Initial_Height = 64 ft

Second bounce

x = 2

36 ft = 64 ft * (e) ^ (2*k)

(e) ^ (2*k) = 0.5625

2 * k = ln (0.5625)

k = - 0.2877

Fourth bounce

x = 4

Height = 64 * (e) ^ (-0.2877 * (4))

Height = 20.248 ft