Question 1043565
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?
<pre>This situation depicts a sequence with {{{a[1]}}} being 30, r being {{{4/5}}}, and {{{a[n]}}} being 5 (< 6). 
We then have: {{{a[n] = a[1]r^n}}} 
{{{5 = 30(4/5)^n}}} 
{{{5/30 = (4/5)^n}}}_____{{{1/6 = (4/5)^n}}}
{{{log (4/5, (1/6)) = n}}}
{{{log (1/6)/log(4/5) = n}}}
n, or number of bounces = 8.029626932, or {{{highlight_green(n = 8)}}}