We know that each bounce reaches 80% of the height of the previous bounce.
So, when it has an initial height of 10 feet, the heights of the subsequent bounces are:
[tex]\begin{gathered} n=1\colon10\cdot80\%=10\cdot0.8 \\ \\ n=2\colon(10\cdot0.8)\cdot80\%=10\cdot0.8\cdot0.8=10(0.8)^{2} \\ \\ n=3\colon(10\cdot0.8^2)\cdot80\%=10\cdot0.8\cdot0.8\cdot0.8=10(0.8)^{3} \end{gathered}[/tex]
Thus, in the given function:
[tex]h(n)=10(0.8)^n[/tex]
The number "10" stands for the initial height of the ball, in feet.
Therefore, if the ball is dropped from 3 feet, we need to replace 10 with 3. We obtain:
[tex]h(n)=3(0.8)^n[/tex]
