Question

a ball is dropped from a height of 25 feet and allowed to bounce until it comes to a rest. each time the ball bounces it rebounds to $\frac{4}{5}$ of its previous height. drag tiles to create an expression you could use to find the height to which the ball rebounds after it hits the floor the third time. 25 4 $\frac{4}{5}$ 3

Explanation:

Step1: Initial - height and bounce - ratio

The ball is dropped from an initial height of 25 feet and the bounce - ratio is $\frac{4}{5}$.

Step2: First bounce height

After the first bounce, the height $h_1$ is $25\times\frac{4}{5}$.

Step3: Second bounce height

After the second bounce, the height $h_2$ is $25\times\frac{4}{5}\times\frac{4}{5}=25\times(\frac{4}{5})^2$.

Step4: Third bounce height

After the third bounce, the height $h_3$ is $25\times\frac{4}{5}\times\frac{4}{5}\times\frac{4}{5}=25\times(\frac{4}{5})^3$.

Answer:

$25\times(\frac{4}{5})^3$