We have the height of the first two bounces. The first one is 6 feet, while the second is 4 feet. We need to find the ratio between the first and second bounces:
[tex]\text{ratio}=\frac{4}{6}=\frac{2}{3}[/tex]
Therefore the equation for the bounces is:
[tex]\begin{gathered} h(n)=6\cdot(\frac{2}{3})^{n-1} \\ h(n)=6\cdot(\frac{2}{3})^n\cdot(\frac{2}{3})^{-1} \\ h(n)=6\cdot(\frac{2}{3})^n(\frac{3}{2}) \\ h(n)=9\cdot(\frac{2}{3})^n \end{gathered}[/tex]
