Aball is dropped from a height of 12 feet returns to a height that is 1/2 of the height from which it fell. the ball continue to bounce half the height of the previous bounce each time. how far will the ball have traveled when it hits the ground the fifth time

Step-by-step explanation:

I'm not sure if you're asking the total amount of feet it will have traveled in 5 bounces, or if you're asking how far the ball will travel on its 5th bounce.  I think it's the latter you want answered, so here goes.

This is an exponential equation, of the form

 where a is the initial height and b is the decay factor.  Our initial height is 12 feet, and since it comes up 1/2 of its previous height each time it bounces, b = 1/2.  Our equation, then, is

If you want to find out how far it drops on the fifth bounce, sub in a 5 for x and solve for y:

which gives you a height of .375 feet which is 3/8 of a foot.

17 1/3

step-by-step explanation: