Solution to the exponential decay equation
==========================================

The solution to the exponential decay equation is the product of the initial quantity
and the the ratio of the current time to the half-life of the quantity, raised to the
power of 2. In other words, for every half-life that passes, the quantity decays by a
factor of 2.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Exponential_decay#>`__.

.. py:currentmodule:: symplyphysics.laws.nuclear.law_of_half_life

.. py:data:: final_quantity

    Quantity that still remains and has not decayed after :attr:`~time` :math:`t`.

Symbol:
    :code:`X`

Latex:
    :math:`X`

Dimension:
    :code:`any_dimension`


.. py:data:: initial_quantity

    Initial quantity that will decay.

Symbol:
    :code:`X_0`

Latex:
    :math:`X_{0}`

Dimension:
    :code:`any_dimension`


.. py:data:: half_life

    :attr:`~symplyphysics.symbols.nuclear.half_life` of the decaying quantity.

Symbol:
    :code:`t_1/2`

Latex:
    :math:`t_{1/2}`

Dimension:
    :code:`time`


.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: law

    :code:`X = X_0 * 2^(-t / t_1/2)`


    Latex:
        .. math::
            X = X_{0} \cdot 2^{- \frac{t}{t_{1/2}}}