Geology Reference
In-Depth Information
To solve this equation, it is helpful to define
w
=
f
m
-
f
. Then, using differentials,
d
w/
d
t
=−
d
f/
d
t
and Eq. (C.4) becomes
d
w
d
t
=−
w
τ
.
This is the classic equation describing exponential decay, with the solution (Section A.1)
w
=
w
0
exp (
−
t/τ
)
.
When
t
=
0,
f
=
0, so
w
0
=
f
m
. Now substituting the definition of
w
, we get
f
m
−
f
=
f
m
exp (
−
t/τ
)
or
f
m
1
t/τ
)
,
f
=
−
exp (
−
(C.5)
which is Eq. (10.7).