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 • x3
The height after the 3rd bounce is 16 so let's set the two expressions equal.
250x3 = 16
x3 = 16/250
Let's change that to a decimal so I can
take the third root with my calculator x3 = 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