How is half-life related to the decay constant?

Here, the decay constant is
,
the half-life is *T*,
is the starting number of parent atoms,
and ``*ln*'' means natural logarithm (as opposed to the logarithm in
base 10).

How can we date rocks, if we know the number of parent and daughter atoms and the decay constant?

Here,
is the decay constant,
*P*(*t*) is the number of ``parent'' atoms at time *t*,
*D*(*t*) is the number of ``daughter'' (why not son?) atoms at time
*t*, ``*ln*'' again means natural logarithm,
and *t* is the age of the rock.