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This is a broad overview of the material that has been covered this semester.
It is not a
formal review but will provide good practice for the exam.
Know how to at least do all
of the following problems.
Solve following differential equation:
2.2:1)
2.2:2)
2.2:3)
2.3:2) A tank initially contains 120L of pure water.
A mixture containing a concentration
of
γ
g/L of salt enters the tank at a rate of 2 L/min, and the wellstirred mixture leaves
the tank at the same rate.
Find an expression in terms of
γ
for the amount of salt in the
tank any time t.
also find the limiting amount of salt in the tank as t
→∞
.
2.3:7) Suppose that a sum S
0
is invested at an annual rate of return r compounded
continuously.
(a) Find the time T required for the original sum to double in value as a function of r.
(b) Determine T if r = 7%
(c) Find the return rate that must be achieved if the initial investment is to double in 8
years.
2.3:16) Newton’s law of cooling states that the temperature of an object changes at a rate
proportional to the difference between its temperature and that of its surroundings.
Suppose that the temperature of a cup of coffee obeys Newton’s law of cooling.
If the
coffee has a temperature of 200
°
F when freshly poured, and 1 min later has cooled to
190
°
F in a room at 70
°
F, determine when the coffee reaches a temperature of 150
°
F.
2.3:18) Consider an insulated box ( a building, perhaps ) with internal temperature u(t).
According to Newton’s law of cooling, u satisfies the differential equation
where T(t) is the ambient (external) Temperature.
Suppose that T(t) varies sinusiodally;
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 Spring '09
 SARKAR

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