A ping pong ball is released from a height of 60 centimeters (cm) and bounces to a height that is 3/4 the previous height. What function est

Question

A ping pong ball is released from a height of 60 centimeters (cm) and bounces to a height that is 3/4 the previous height. What function estimates the height, H, in cm of the ping pong ball after x bounces?

Enter a number in each blank to correctly complete the function.

H = BLANK(BLANK)^x

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MichaelMet 5 months 2021-08-18T08:31:48+00:00 1 Answers 0 views 0

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    2021-08-18T08:33:47+00:00

    Answer:

    H = 60(3/4)^x

    Step-by-step explanation:

    After each bounce, the height it reach is 3/4 the previous one.

    Let the height of nth bounce be denoted as h_n and the first bounce is h_1.

    We are given that h_1 = 60 cm. Following the rule in the problem, we get:

    h_2 = (3/4)h_1 = (3/4)60

    h_3 = (3/4)h_2 = (3/4)*(3/4)60 = 60(3/4)^2

    h_4 = (3/4)h_3 = (3/4)*60(3/4)^2= 60(3/4)^3

    We see that h_n = 60(3/4)^n is the formula for the height for the nth bounce. Therefore, H = 60(3/4)^x is the answer.

    I hope this helps! 🙂

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