Aball is dropped from a height of 10 meters. each time it bounces it reaches 50 percent of its previous height. what is the total distance it reaches after 5 times

A good equation for this is 10*.5^x
In this case,x=5
If we solve 10*.5^x we get 0.3125 as our answer.

Original height 10 meters

first bounce
10/2 = 5 meters

second bounce
5/2 = 2.5 meters

third bounce
2.5/2 = 1.25 meters

fourth bounce
1.25/2 = 0.625 meters

fifth bounce 
0.625/2 = 0.3125 meters