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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.

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 f class=

Answer :

As given by the question

There are given that the first bounce is 6.7.

Now,

81% of the first bounce is:

[tex]6.7-\frac{81}{100}=1.273[/tex]

The,

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

So,

[tex]6.7+1.273=7.973[/tex]

Now,

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

So,

[tex]\begin{gathered} 7.973-\frac{81}{100}=1.5148 \\ 7.973+1.5148=9.4878_{} \end{gathered}[/tex]

The third bounce is 9.4878 ft

Now,

For the fourth bounce

[tex]\begin{gathered} 9.4878-\frac{81}{100}=1.8026 \\ 9.4878+1.8026=11.29 \end{gathered}[/tex]

Now,

For the fifth bounce

[tex]\begin{gathered} 11.29-\frac{81}{100}=2.14 \\ 11.29+2.14=13.435 \end{gathered}[/tex]

Now,

For the sixth bounce:

[tex]13.43-\frac{81}{100}=2.546[/tex]

So, the height of the sixth bounce is 2.546

Hence, the correct option is C

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