The oxytocin loop

You will write a model of the positive feedback of birth. Each round of contractions multiplies the strength by a gain, until the strength is enough to push the baby out.

The idea. After $n$ rounds, the strength is the first strength times the gain, $n$ times over. Birth needs $100$ units.

Your tasks.

1. Finish strength_after. It gives the strength after n rounds.
2. Finish rounds_needed. It counts the rounds until the strength reaches needed.
3. Finish rounds_for_each. It gives a list with the rounds needed for each gain in a list, starting from the same strength.