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# Linear Recurrence Relations

Take your recursion skills to the next level. If you've got a recurrence relation but no computer, how can you find a closed form? What about asymptotic behavior? How fast do rabbits reproduce?

- There are 10 stages to pass through.
- For passing through the first stage, 50 points are given.
- For passing through the \( n^{\text{th}} \) stage, additional \( (5n + 20) \) points are given, where \(n=2, 3, \ldots, 9, 10.\)

If someone passes through all 10 stages, what is the final score?

1) Only one disk at the top of a stack can be moved at a time.

2) No disk can be placed on top of a smaller disk.

What is the minimum number of steps required to move a tower of 7 disks?

**Details and assumptions**

- There can be colors not used.

Assume that the flask is large enough to contain any number of bacteria.

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