MATHEMATICS AND PHYSICAL SCIENCES DEPARTMENT
Long Quiz 4 in COE0019 Differential Equations
3rd Term S.Y. 2022-2023
Name:
Faculty Name:
Section:
___________________________________ Student No.:
___________________________________ Date of Examination:
___________________________________ Schedule (Time/Day)
_______________
_______________
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Pledge of Honor
I, _________________________, a student of the FEU – Institute of Technology, pledge to exercise integrity
and honesty as I take this examination. I consider it dishonest to ask for, give, or receive help in this
examination.
I pledge to do all that is in my power to live a life of dignity and credibility and to create that spirit in my
environment.
_____________________________
Student’s Signature
_____________________________
Date
GENERAL INSTRUCTIONS:
1. Read, understand, and analyze each problem. Write your final answer in the box provided after each problem.
2. Using extra sheets, show your clear and complete solution. Use black or blue ink pen only for your solution.
3. This exam must be submitted on July 14, 2023, at 11:00 AM during the start of the Final Examination in
COE0019. Late submissions will not be accepted.
4. This is an ALL OR NOTHING EXAM. An item answered correctly will receive 10 points while an item answered
incorrectly or with no clear solution will receive 0 point.
1. A detective is called to the scene of a crime where a dead body has just been found. She arrives on the
scene at 10:23 P.M. and begins her investigation. Immediately, the temperature of the body is taken and is
found to be 80°F. The detective checks the programmable thermostat and finds that the room has been kept
at a constant 68°F for the past 3 days. After evidence from the crime scene is collected, the temperature of
the body is taken once more and found to be 78.5°F. This last temperature reading was taken exactly one
hour after the first one. Determine the time of death of the victim.
2. Of the 1500 guests, crew, and staff that spend their vacation in Boracay, 5 have the flu. After one day in the
island, the number of infected people has risen to 10. Assuming that the rate at which the flu virus spreads
is proportional to the product of the number of infected individuals and the number not yet infected, determine
how many people will have the flue at the end of the 14-day island trip.
3. A tank contains 8 liters of water in which 32 grams of chemical is dissolved. A solution containing 2 g/L of the
chemical flows into the tank at a rate of 4 L/min, and the well-stirred mixture flows out at a rate of 2 L/min.
What is the concentration of chemical in the tank after 20 minutes?
4. A person places PhP 50 000 in an account that accrues interest compounded continuously. Assuming no
additional deposits or withdrawals, how much will be in the account after 10 years if the interest rate is a
constant 8.3% for the first four years and a constant 9.5% for the last years?
5. A rock of mass 5 kg is dropped from rest in a viscous fluid. If the resisting force from the fluid is 0.002v where
v is the instantaneous velocity in m/s, what is the distance travelled by the rock after 5 seconds? Use g =
9.81 m/s.
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6. The charge, Q, at any given time t for a certain RC circuit is defined by Q(t) = 4te!"" . Determine the maximum
charge of the circuit.