A golf ball is manufactured so that if it is dropped from A feet above the ground onto a hard surface, the maximum height of each bounce will be one half of the height of the previous bounce
a. Find an exponential equation that gives the height hthe ball will attain during the nth bounce.
h=
b. If the ball is dropped from 9 feet above the ground onto hard a surface, how high will it bounce on the 4th bounce?On the 4th bounce, the ball will reach a height of feet.

An exponential equation that gives the height ball will attain during the nth bounce is .

On the 4th bounce, the ball will reach a height of feet.

Given:

The maximum height of each bounce will be one half of the height of the previous bounce

Let: The maximum height of the ball is h.

In the first bounce:

Maximum height =

In the second bounce:

Maximum height =

In the third bounce:

Maximum height =

in the bounce

Maximum height =

(a)

(b) h = 9 feet, n = 4

Maximum height = feet

Therefore, On the 4th bounce, the ball will reach a height of feet.

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Step-by-step explanation:

a.) To model this scenario

Let the height of ball = y

The height of 1st= 0.5y

2nd =0.5(0.5y)

3rd = 0.5*(0.5(0.5y))

Hence the height of nth bounce can be modeled as

Height of nth bounce =(0.5ⁿ-1)*y

The exponential equation is

hn= (0.5ⁿ-1)*y

b.) if the ball is dropped from 9ft above the ground

y= 9ft

On the 4th bounce

n=4

Substituting in the exponential equation we have

h4=(0.5^4-1)*9

h4=0.5³*9

h4= 0.125*9

h4= 1.125ft

On the 4th bounce, the ball will reach a height of 1.125ft

they are simplified

step-by-step explanation: