Let's first find the common ratio of the geometric sequence.
The height of the ball after the first bounce is given as 500 meters.
Let's call this height "h".
The height of the ball after the second bounce is given as h*r, where "r" is the common ratio.
Similarly, the height of the ball after the third bounce is h*r*r.
From the information in the table, we can see that each bounce decreases the height by 1/2.
Therefore, the common ratio "r" is 1/2.
To find the height of the ball after the 8th bounce, we need to calculate h*(1/2)^7.
Substituting h = 500, we get 500*(1/2)^7 = 500*(1/128) = 3.90625 meters.
Rounding this to the nearest meter gives us an answer of 4 meters.
Therefore, the ball bounces to a height of 4 meters on the 8th bounce.
A ball is dropped from a height of 500 meters. The table below shows the height of each bounce, and the heights form a geometric sequence. How high does the ball bounce on the 8th bounce? Round your answer to the nearest meter.
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