My grandma was so impressed with the movement of her arcade that she decided to study the movement of other buildings along the fault, in particular, the only other arcade in town. This arcade, it was discovered, has been moving in a very similar fashion to that of my grandma's arcade. The rival arcade is located where the functions y = x and x-n + y-n = 1 intersect (n is the number of earthquakes). The diagram below shows the movement of the rival arcade after the first and second earthquake. My grandma was suspicious that these movements might be similar to those of her arcade, but first she wanted to know where her rivals are going.

The curve of the graph for the opposing arcade as n increases moves closer and closer to the point (1,1) similar to Grandma's arcade.

This chart shows the distances the rival arcade moves between earthquakes.

Earthquake Distance Moved
2

9.49

3 2.50
4 1.15
5

0.66

6 0.43
7 0.30
8 0.22
9 0.17
10 0.13

With this information my Grandma was able to make the prediction that the rival arcade will move closer and closer to the point (1, 1) but will never touch that point for the same reason that her arcade touches the point (1,1). If you don't remember click here. This prompted my Grandma to ask me a new question, as whether or not the movements of both arcades have some similarities.