Answer: The correct option is (b) 4.1 feet.
Step-by-step explanation: Given that a tennis ball is dropped from a height of 8 feet. After the ball hits the floor, it rebounds to 80% of its previous height.
We are to find the height to which the ball will rebound after its third bounce.
The height to which the ball rebound after first bounce is
[tex]h_1=80\%\times 8=\dfrac{80}{100}\times 8=6.4~\textup{feet}.[/tex]
The height to which the ball rebound after second bounce is
[tex]h_1=80\%\times 6.4=\dfrac{80}{100}\times 6.4=5.12~\textup{feet}.[/tex]
The height to which the ball rebound after third bounce is
[tex]h_1=80\%\times 5.12=\dfrac{80}{100}\times 5.12=4.096~\textup{feet}.[/tex]
Therefore, the ball will rebound to a height of 4.096 feet after third bounce.
Rounding to the nearest tenth, the required height will be 4.1 feet.
Option (b) is correct.
