Question

A ball bounces to a height of 6.1 feet on the first bounce. Each subsequent bounce reaches a height that is 82% of the previous bounce. What is the height, in feet, of the fifth bounce? Round your answer to the thousandths place.

Answer 1

In the first bounce, the height is

`6.1*(0.82)^0=6.1`

In the second bounce, the height is

`6.1*(0.82)^2=5.002`

Then, we can note that the pattern is

`6.1*(0.82)^(n-1)`

where n represents the number of bounces of the ball. Then, for n=5 (fifth bounce), we get

`\begin{gathered} 6.1*(0.82)^(5-1) \\ 6.1*(0.82)^4 \end{gathered}`

which gives

`6.1*(0.82)^4=2.7579`

Therefore, by rounding to the nearest thousandths, the answer is 2.758 feet