Question

A ball is dropped from a height of 30 feet and each time it hits the ground it bounces 0.75 of the previous height. What is the height of the ball after it makes its third bounce? Round to the nearest hundredth of a foot.

Answer 1

Answer:

its 12.66 feet

Step-by-step explanation:

Answer 2

If the ball is "starting" at 30 feet, then to get how high it went the bounce, we simply multiply 0.75 times 30, and to get the next bounce's height, is again (30*0.75)0.75, and so on.

so... the 0.75 or 3/4 is our "multiplier" to get the next term's value, or our "common ratio".  So is just a geometric sequence, if the first term is 30, the common ratio is 0.75, what's the 4th term?  Because the first bounce happens after the 30 feet, at the 2nd term, thus the 4th term is the 3rd bounce.

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=30\\ r=0.75\\ n=4 \end{cases} \\\\\\ a_4=30\cdot (0.75)^{4-1}\implies a_4=30(0.75)^3$