A tennis ball is dropped from a height of 80 feet. After the first bounce, the ball reaches a height of 48 feet. After the second bounce, the ball reaches a height of 28.8 feet. After the third bounce, the ball reaches a height of 17.3 feet. Each time the ball hits the ground it only bounces up to 60% of the original height. By what factor is the ball's height changing after each bounce?

The factor is 0.60

Step-by-step explanation:

we know that

The expression that model this situation is a exponential equation of the form

where

h is the height of the ball in feet

x is the number of bounces

a is the initial height

b is the factor

we have

so

Verify

First bounce

For x=1

---> is ok

Second bounce

For x=2

---> is ok

Third bounce

For x=3

---> is ok

therefore

The factor is 0.60

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign