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The correct solution in this case is the impulse function, since
the gasoline all enters the reservoir at once.
Why not a step function?
The step function does not represent this situation very well.
Remember that a step input function is used to represent input that
starts and then continues steadily over a period of time. Here,
once the tank falls into the reservoir, the gasoline enters the lake
nearly instantly. There is no further input of contaminant after
the initial surge. An example of a step function is the
earlier question about the electroplating company
which starts operation and begins sending a relatively constant amount
of nickel into a nearby stream.
You may want to
review the differences between the types of input
functions now before you go on. Try coming up with your own
examples of both step input functions and impulse input functions.
Go on
John Hoggard <hoggard@math.vt.edu>
Last modified: Sun Aug 10 17:43:06 EDT 1997