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In Example 5, the ratios of consecutive terms are not equal.
So, the pattern is not exponential.
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Rewrite the table using 1-second intervals. Each first difference tells you how much the distance increased during 1 second, or the speed of the shot put ball. Each second difference tells you how much the speed of the shot put ball increased during 1 second.
First differences: changes in distance
Second differences: changes in speed
As you can see, the speed is increasing by 32 feet per second each second. You can summarize this information in a table. (Note that at 0 seconds, the speed is 0 feet per second because you have not dropped the ball yet.)
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