Question

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

Answer 1

Answer:

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