Two feedback loops

A negative loop pushes a level towards a set point. A positive loop multiplies a level in each cycle. You will write one step of each loop and then run them.

The idea. In the negative loop, each step adds $0.3$ times the gap between the set point and the level. In the positive loop, each cycle multiplies the level by $1 + \text{gain}$.

Your tasks.

1. Finish negative_step. It gives the new level after one step.
2. Finish settle. It starts at start, applies negative_step the given number of times and gives the final level.
3. Finish cycles_to. It counts the cycles of the positive loop until the level is at least need.