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Calculus II (MAT 146)Dr. Day Wednesday, Oct 21,
2015
Applications of Differential Equations (Chapter 9)
Wednesday, Oct 21, 2015
MAT 146
MAT 146
Applications!
Wednesday, Oct 21, 2015
Rate of change of a population P, with respect to time t, is proportional to the
population itself.
MAT 146
Applications!
Wednesday, Oct 21, 2015
The radioactive isotope Carbon-14
exhibits exponential decay. That is,
the rate of change of the amount
present (A) with respect to time (t)
is proportional to the amount
present (A).
MAT 146
Applications!
Wednesday, Oct 21, 2015
MAT 146
Applications!
Wednesday, Oct 21, 2015
The security staff at a rock concert found a dead body in a mezzanine restroom, the apparent victim of a fatal shooting. They alert the police who arrive at precisely 12 midnight. At that instant, the body’s temperature is 91º F; by 1:30 a.m., 90 minutes later, the body’s temperature has dropped to 82º F. Noting that the thermostat in the restroom was set to maintain a constant temperature of 69º F, and assuming the the victim’s temperature was 98.6º F when she was shot, determine the time, to the nearest minute, that the fatal shooting occurred. Assume that the victim died instantly and that Newton’s Law of Cooling holds. Show all appropriate evidence to support your solution.
MAT 146
Applications!
Wednesday, Oct 21, 2015
MAT 146Wednesday, Oct 21, 2015
MAT 146Wednesday, Oct 21, 2015
MAT 146
Applications!
Wednesday, Oct 21, 2015
MixturesA tank contains 2000 L of brine with 30 kg of dissolved salt. A solution enters the tank at a rate of 20 L/min with 0.25 kg of salt per L . The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes? After 60 minutes?
MAT 146
Applications!
Wednesday, Oct 21, 2015
MixturesA tank contains 1000 L of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes? After 20 minutes?
MAT 146
Applications!
Wednesday, Oct 21, 2015
Spreading a Rumor: Suppose that y represents the number of people that know a rumor at time t and that there are M people in the population. For these parameters, one model for the spread of the rumor is that “the rate at which the rumor is spread is proportional to the product of those who have heard the rumor and those who have not heard it.”
MAT 146
Application: Ice Growth
Wednesday, Oct 21, 2015
Details . . . details . . . details!
https://plus.maths.org/content/teacher-package-differential-equations
