The correct solution in this case is the impulse function, since
the gasoline all enters the reservoir at once.
The sinusoidal function does not represent this situation
well.
Remember that a sinusoidal input function is used to represent input
which increases decreases on a regular basis, such as the
example of the
wastewater treatment plant,
which is discussed under the
lesson on modeling. It released
varying amounts of ammonia into a lake over the course of a day, and
was represented by a sinusoidal function. You might look at this
section on modeling if you haven't
already.
Since nothing is periodic here, it doesn't make sense to use a sinusoidal function.
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 input that would be sinusoidal and input that would be impulse functions.