Question

Suppose a ball is dropped from an initial height of 10 feet and loses 40% of its height after every bounce. Complete the table to give the heights of the ball after the first 4 bounces. Bounce Height after Bounce 1 ? 2 ?3 ?4 ?Write the equation for the height of the ball, y, after x bounces, and fill out the chart.

Answer 1

`y=10(0.9)^x`

Step-by-step explanation:

The ball is dropped from an initial height of 10 feet.

It loses 10% of its height after every bounce.

• An equation for the height of the ball, y, after x bounces is derived below:

`\begin{gathered} y=10(1-10\%)^x \\ y=10(1-0.1)^x \\ y=10(0.9)^x \end{gathered}`

Substitute the values of x=1,2,3 and 4 respectively:

`\begin{gathered} When\; x=1,y=10(0.9)^1=9\text{ feet} \\ When\; x=2,y=10(0.9)^2=8.1\text{ feet} \\ When\; x=3,y=10(0.9)^3=7.29\text{ feet} \\ When\; x=4,y=10(0.9)^4=6.561\text{ feet} \end{gathered}`