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?
1 answer
Question:
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?
Answers
Answer:The factor is 0.60Step-by-step explanation:we know thatThe expression that model this situation is a exponential equation of the form[tex]h=a(b^x)[/tex]whereh is the height of the ball in feetx is the number of bouncesa is the initial heightb is the factorwe have[tex]a=80\ ft\\b=60\%=60/100=0.60[/tex]so[tex]h=80(0.60^x)[/tex]VerifyFirst bounceFor x=1[tex]h=80(0.60^1)=48\ ft[/tex] ---> is okSecond bounceFor x=2[tex]h=80(0.60^2)=28.8\ ft[/tex] ---> is okThird bounceFor x=3[tex]h=80(0.60^3)=17.28\ ft[/tex] ---> is okthereforeThe factor is 0.60
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