Answer:
Part a)

Part b)
Check the attached figure to see the ultimate behavior of the graph.
Part c)
The level = 25, Amplitude = 0.2499
Step-by-step Solution:
Part a)
Given:

Rate in:

Rate out:

So, the differential equation would become:

Rewriting the equation:

As
is the coefficient of
, while
is the constant term in the right side of the equation:


First it is important to determine the function
:



The general solution then would become:




Evaluate at 

Solve to c:








Therefore, the general solution then would become:

Part b) <em>Plot the Solution to see the ultimate behavior of the graph</em>
The graph appears to level off at about the value of
.
The graph is attached below.
Part c)
In the graph we note that the level is
.
Therefore, the level = 25
The amplitude is the (absolute value of the) coefficient of
in the general solution (as the coefficient of the sine part is a lot smaller):
Therefore,

Keywords: differential equation, word problem
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