The thyroid feedback loop

A simple model of the thyroid uses levels where 1 is the normal level. TSH falls as the thyroid hormone rises. The thyroid makes hormone in proportion to TSH and to its capacity, and a little hormone is cleared at every step. You will build the loop and find where it settles.

The idea. A negative feedback loop settles at a steady level. A smaller capacity, as in a lack of iodine, settles at a lower hormone level and a higher TSH.

Your tasks.

1. Finish tsh_from. It gives TSH as $2$ divided by $(1 + \text{hormone})$.
2. Finish step. The thyroid makes capacity * tsh. The new level is the old level plus $0.2$ times the difference between the amount made and the old level.
3. Finish settle. It starts at a level of $1.0$, applies step $100$ times and gives the final level.