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

Answer 1

H = 60(3/4)^x

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! :)