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).
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