Question 1043565
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a ball is dropped from a height of 30 feet.each time it strikes the ground, it bounces up to 4/5 of the previous height. 
How many times does the ball hit the ground before it bounces up less than 6 feet?
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<pre>
# of hit/bounce   height of bouncing
0	          30.00
1	          24.00
2	          19.20
3	          15.36
4	          12.29
5	           9.83
6	           7.86
7	           6.29
8	           5.03
9	           4.03


Geom. progression. {{{h[0]}}} = 30, common ratio r = {{{4/5}}}.

{{{h[n]}}} = {{{30*(4/5)^n}}}, n = 1, 2, 3, . . . height after n-th bounce.

Your n is 7.
</pre>

On geometric progressions, read the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A>

in this site.