Drug Absorption
===============

When a drug is administered to a pacient it follows a process of progressive absorption in the patient's body.
Its concentration increases each day according to a model that depends on the concentration of the drug in the body that day `n` (:math:`y_n`), the absorption rate (:math:`k`) and the initial drug concentration (:math:`y_0`).

   .. math::

      \begin{aligned}
      y_{i+1} &= y_i + k \cdot y_i \cdot (1 - y_i), \quad i>=1
      \end{aligned}
   
For example, :math:`y_0 = 0.4` and :math:`k = 0.5` the first terms of the succession are:

   .. math::

      \begin{align*}
      y_0 &= 0.4 \\
      y_1 &= 0.52 \\
      y_2 &= 0.6448 \\
      y_3 &= 0.7593164800000001 \\
      \end{align*}

The concentration is considered `stable` when the drug concentration is `equal` to the previous day `under the given tolerance`.

You are asked to deliver the folowing function in the :mod:`drug_abs` module (:file:`drug_abs.py` file):

.. py:function:: drug_abs_days(y0, k, eps)

   :param float y0: Initial drug concentration, :math:`0.0 < y0 < 1.1`.
   :param float k: Absorption rate, :math:`0.0 < k < 1.1`.
   :param float eps: Tolerance. :math:`eps <= 0.1`.
   :return: Number of days needed by the drug to stabilize for the given tolerance.
   :rtype: int

For example:

.. literalinclude:: drug_abs_days.test
    :language: pycon
    :start-after: --ini
    :end-before: --fi

Doctests are available in the file :download:`drug_abs_days.test`.