Differential Equations
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mat239_differential_equations.docxMAT239 Differential Equations
Problems 1.1-1.11
This will be graded for correctness. Most problems are chosen from the course notes. For problems 1. and 2. use the ideal models and NOT the models that best fit your data. The ideal model is given in the statement of the problem.
1. The rate of change of M & M’s is decreasing by half of the M & M population. Let’s start with 103 M & M’s.
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(a) Problem 1.2c: State the differential equation that models the M & M population.
2. The rate of change of M & M’s is decreasing by half of the M & M population and then 10 M & M’s are added for every value of time. Again let’s start with 103 M & M’s.
· (a) Problem 1.4c: State the differential equation that models the M & M population.
· (b) Problem 1.4e: Solve the DE from (a) to get an equation for the amount of M & M’s at any time. Show ALL work
3. The rate of change of bacteria M is increasing by 30% every hour and then 5 mg of bacteria are removed every hour. There is 60 mg of bacteria to start.
(a) Problem 1.7c: State the differential equation that models the bacteria population.
(b) Problem 1.7e: Solve the DE from (a) to get an equation for the amount of bacteria at any time. Show ALL work
4. It was noon on a cold December day in Tampa, Florida 16◦C. Detective Taylor arrived at the crime scene to find the sergeant leaning over the a dead body. The sergeant said that there were several suspects and if they knew the time of death they could narrow the list. Detective Taylor took out a thermometer and measured the temperature of the body to be 34.5◦C. He then left for lunch. Upon returning at 1 pm he found the body to be 33.7◦C. The detective knows that the rate at which the temperature of a body changes is proportional to the difference between the temperature of the body and the outside temperature. If normal body temperature is 37◦C, then when did the murder occur?
