Estimation and Limits -- A More Precise Look --
Stretch Your Understanding
Many lakes contain some natural contaminants. Suppose that Long Lake
originally contained some of the same contaminant that was dumped into the lake
by the Fly-by-Night Toxic Waste Disposal Company. In this case
the amount of this contaminant in the lake might be described by a dynamical
system like
p(1) = 10 ppm
p(n) = 0.9 p(n - 1) + 0.005
- What is the natural level of this contaminant in Long Lake?
- In this situation we can only ask that the level of contaminant drop
to within some tolerance of its natural level. When will the level of this
contaminant be within 0.1 ppm of ts natural level?
- When will the level of this contaminant be within 0.01 ppm
of its natural level?
Copyright c 1995 by
Frank Wattenberg, Department of Mathematics, Carroll College,
Helena, MT 59625