When a ball is dropped, the height it reaches after it bounces is a fraction of its original drop height. The expression shown for each ball gives the fraction of the
drop height that the ball reaches after x bounces. What fraction of its original
height does each ball bounce up to after the third bounce?
a. basketball:(3/4)with an exponent of x
b. tennis ball: (2/3) with an exponent of x
c. softball: (3/10)with an exponent of x

Let's assume that the ball is dropped from a height X. After every bounce, the ball loses 1/4th of its initial height. So for the first bounce, it comes up to 3/4 times X. For the second one it comes up to 3/4 * 3/4= 9/16 times X, similarly for the third time it comes up till 9/4 * 3/4= 27/64 times X.. Adding all these distances, for the distance travelled by the ball after bouncing.. therefore the distance is 3/4 + 9/16 + 27/64 = 111/64 times X.. but the ball travels equal distance while going down too, so the total distance travelled is 111/64 * 2 = 222/64 or 111/32 times X.. or about 3.46 times the initial height of the ball..

Hence, the ball will travel 3.46 times its initial heights after 3 bounces.

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step-by-step explanation: