Question

A ball bounces to a height of 6.7 feet on the first bounce. Each subsequent bounce reaches a height that is 81% of the previous bounce. What is the height, in feet, of the sixth bounce? Round your answer to the thousandths place.

Answer 1

As given by the question

There are given that the first bounce is 6.7.

Now,

81% of the first bounce is:

`6.7-(81)/(100)=1.273`

The,

The next bounce is the addition of 81% of the first bounce

So,

`6.7+1.273=7.973`

Now,

The third bounce is addition of 81% of the second bounce

So,

`\begin{gathered} 7.973-(81)/(100)=1.5148 \\ 7.973+1.5148=9.4878_{} \end{gathered}`

The third bounce is 9.4878 ft

Now,

For the fourth bounce

`\begin{gathered} 9.4878-(81)/(100)=1.8026 \\ 9.4878+1.8026=11.29 \end{gathered}`

Now,

For the fifth bounce

`\begin{gathered} 11.29-(81)/(100)=2.14 \\ 11.29+2.14=13.435 \end{gathered}`

Now,

For the sixth bounce:

`13.43-(81)/(100)=2.546`

So, the height of the sixth bounce is 2.546

Hence, the correct option is C