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Nt1310 Unit 7 Lab Report

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Unfortunately, if we want to know how many moves it will take to transfer 100 disks from pole A to pole B, we will first have to find the moves it takes to transfer 99 disks, 98 disks, and so on and so forth. Therefore the recursive pattern will not be much help in finding the time it would take to transfer all the disks.
However, the recursive pattern can help us generate more numbers to find an explicit (non-recursive) pattern. Here's how to find the number of moves needed to transfer larger numbers of disks from pole A to pole C, remembering that n equals the number of moves needed to transfer n-1 disks from post A to post C:
1.For 1 disk it takes 1 move to transfer 1 disk from post A to post C;
2.For 2 disks, it will take 3 moves: 2n + 1 = 21 + 1 = 3
3.For 3 disks, it will take 7 moves: 2n + 1 = 23 + 1 = 7
4.For 4 disks, it will take 15 moves: 2n + 1 = 27 + 1 =15
5.For 5 disks, it will take 31 moves: 2n + 1 = 215 + 1 =31
6.For 6 disks... …show more content…

In the following graph, the exponential function has a very similar trend to the trend of y=2x. It is important to note that the exponential function is actually y=ax where a > 0. Using y=1x would only produce a horizontal line. Therefore the next value used was y=2x. In order to make the function fit better with the points we make transformations that slightly change the function. The first step is to lower the line so that the line can become closer to the data points. With this data set it sloa stands to reason that there are negative numbers very much possible. It would work in the exponential equation 2x-1.

Conclusion Thanks to the legend of the Tower of Hanoi, if one disc was transferred every second since the beginning of time, it would take about 580 billion years until the puzzle is solved and the world comes to an end. If this were true, then the world still has many more years to

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