#1**0 **

Let's call the fraction that it bounces back up "x"

After the 1st bounce, the ball is 250 • x high

&, after the 2nd bounce, the ball is (250 • x) • x high

&, after the 3rd bounce, the ball is [ (250 • x) • x ] • x high

All those parentheses aren't necessary, I just included them as a visual

to show that each bounce is x times the height of the previous.

So.... anothe way of writing the height after the 3rd bounce is 250 • x^{3}

The height after the 3rd bounce is 16 so let's set the two expressions equal.

250x^{3} = 16

x^{3} = 16/250

Let's change that to a decimal so I can

take the third root with my calculator x^{3} = 0**.**064

Take the third root and obtain x = 0**.**4

And, of course, 0**.**4 = 2/5 so the answer is .... wait for it ..... **B. 2/5**

_{.}

Guest Aug 30, 2020