Biology Reference
In-Depth Information
233
SIMPLE DIFFERENTIAL EQUATION
From the definition of e, the solution of the following differential equation:
dy/dt = Ay
is simply y = Be
At
, where A and B are constants. This equation is commonly
encounter in many biological processes. For example, a culture of bacteria
grows exponentially can be described for A being positive. If the starting
number of bacteria is N
0
, then B = N
0
. The doubling time is calculated from:
2
=
e
At
,
or
t
= (ln2)/A.
For any decaying process, whether a radioactive material, HIV-1 RNA
molecules in blood of AIDs patients, or other substances, A is negative. In
such cases, a similar calculation gives the half-life.
The above differential equation is classified as linear first order ordinary.
Other differential equations can be of higher order, non-linear, partial, etc.
(see, for example, Taubes, 2001). They can also be converted into integral
equations.
