NAME: __________________________________
SECTION: _______________
PROBLEM SET
Subject/Schedule: MATH 7 / PETENG 1 & 2 / MARCH 24, 2018
Submission Date: March 26, 2018 / on or before 10:00AM
Read and analyze the following problems carefully. Write the complete solution and boxed final answer on Makarโs Paper.
1. A bacterial population follows the law of exponential growth. If between noon and 2:00PM the population triples, at what time
should the population become 100 times when it was noon? At 10:00AM what percentage was present?
2. Forty percent of a substance has decayed after 10 years. How much of the substance remains after 15 years?
3. At a certain time, thermometer reading 70 degrees Fahrenheit is taken outdoors where the temperature is 15 degrees
Fahrenheit. Five minutes later, the reading drops to 45 degrees Fahrenheit. After another five minutes, the thermometer is
brought back indoors where the temperature is fixed at 70 degrees Fahrenheit. What is the thermometer reading ten minutes
after the thermometer is brought back indoors? When will the reading, to the nearest degree, return back to its original reading
of 70 degrees Fahrenheit?
4. An inductance of 1 Henry and a resistance of 2 Ohms are connected in series with an EMF of ๐ธ๐โ๐ก Volts. No current is flowing
initially. (a)If the current is 10 A after 1 second, how much must E be? (b)If E is 50V, when will the current be 5A?
5. A body falls from rest against a resistance proportional to the cube of the speed at any instant. If the limiting speed is 3 m/s, find
the time required to attain a speed of 2 m/s?
6. An object of mass 3 kg is released from rest 500 meters above the ground and allowed to fall under the influence of gravity. The
force due to air resistance is proportional to the velocity of the object with proportionality constant of 3 N-s/m.
7. Find the orthogonal trajectories of the family of circles defined by (๐ฅ โ ๐)2+ ๐ฆ 2= ๐2.
8. A certain radioactive material follows the exponential change and has a half-life of 38 hours. Find how long it takes for the 90%
of the radioactivity to be dissipated.
9. For a certain curve, the point of contact of each tangent to it bisects the part of the normal terminating on the coordinate axes.
Find the equation of the curve.
10. A constant inductance of 1H and a variable resistance R = 5+t, Ohms are connected in series with a constant electromotive
force. If I = 0A at time t = 0s., what is the constant voltage if at t = 5 seconds, the current I = 30 A?
*No late submission.
*This paper serves as the front page.