This lab investigates a typical mixture problem and the effect of different
initial conditions and various run times on the solution of the governing ODE.
The ODE here is based on: rate of change = in - out. i.e.
Problem: A rock contains two radioactive isotopes
and
that belong to the same radioactive series; that is
decays into
which then decays into stable atoms. Assume that the rate that
decays into
is
and that the rate of decay of
is proportional to the mass
of
present. If the decay constant is
using the time periods and initial conditions given below create the graphs of
the particular solutions as indicated using ODE Architect and print each of
the groups 1-4 below (1 print out for each group).
1. For a time lapse of
on the same grid graph the particular solutions for :
Initial conditions:
2. Repeat 1. for 13 sec.
3. Repeat 1. for 23 sec.
4. Repeat 1. for 53 sec. print this graph with the slope field.
5. Now write out a discussion (one page max.) about your observations of what seems to be happening. Include observations as to how the projection changes as the time period increases and how the various initial conditions effect these changes.
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