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?

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calculista calculista · Answer 1 · 2020-04-16T14:39:16+02:00

Answer:

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

[tex]h=a(b^x)[/tex]

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

[tex]a=80\ ft\\b=60\%=60/100=0.60[/tex]

so

[tex]h=80(0.60^x)[/tex]

Verify

First bounce

For x=1

[tex]h=80(0.60^1)=48\ ft[/tex] ---> is ok

Second bounce

For x=2

[tex]h=80(0.60^2)=28.8\ ft[/tex] ---> is ok

Third bounce

For x=3

[tex]h=80(0.60^3)=17.28\ ft[/tex] ---> is ok

therefore

The factor is 0.60