Assignment A2

All students are encouraged to try all exercises, but
3xx Does any two of exc. 1,2 (below), Heath 3.5 a,b (page 153-154)
5xx Does all three exc. 1,2, and Heath 3.5 a,b
If you hand in more than the required solutions your best marks will be counted.

Exc. 1 As seen in the first assignment, different animals emit different amount of heat. From several examples one might want to hypothesize a mathematical relationship between mass (in kg) and metabolized energy (in Watts). The task in this exercise is to study the data below, propose a mathematical model, test it (ie fit to data and see how well it fits) and motivate why it is plausible.

Species
Mass (kg)
Metabolism (W)
Cow
400
 270
Human
 70
 82
Sheep
 45
 50
Hen
 2
 4.8
Rat
 0.3
 1.45
Dove
 0.16
 0.97

Try to plot the data in various ways to find the trend in the data/ (hint try logarithmic plots, what do these tell you?). You can also try some physical reasoning about what property/(ies) will most affect metabolism and emitted heat. matlab data matrix

Exc 2. Three suspected terrorists have been apprehended at the Edmonton international airport. Each suspect was found carrying a radioactive substance. The police is interested in tracing the connections of the three suspects. To their aid there is a set of reference samples collected from the UN international atomic energy inspectors in various countries. Each suspect can have one or more connections, hence Is = a1*Ir1+a2*Ir2+a3*Ir3, where Ir is defined below, and one or more of a1..a3 is non-zero. Note that this equation is dependant on both {a1..a3} and {Ir1..Ir3}.

Suspect 1:

Time
 1
 2
 3
 4
 5
Radioactive Intensity Is1
 2.7731
 2.5720
 2.3936
 2.2354
 2.0952

Suspect 2:

Time
 1
 2
 3
 4
 5
Radioactive Intensity Is2
 1.1921
 1.1843
 1.1765
 1.1688
 1.1611

Suspect 3:

Time
 1
 2
 3
 4
 5
Radioactive Intensity Is3
 1.9843
 1.9686
 1.9532
 1.9378
 1.9225

Through the vigilant efforts of the UN weapons inspector Rolf Ekeus, reference data has been collected from various nuclear production facilities around the world. Each reference sample is from a pure radioactive substance which decays according to the formula:

Where l is the radioactive decay constant and Io the amount at time t=0.

The following lists the radioactive decay of each reference. Note the different time scales:

Time
 2
 4
 6
 8
 10
Radioactive Intensity Ir1
 3.1444
 2.4718
 1.9431
 1.5274
 1.2007



Time
 10
 20
 30
 40
 50
Radioactive Intensity Ir2
 9.2404
 8.5385
 7.8899
 7.2906
 6.7368



Time
 10
 20
 30
 40
 50
Radioactive Intensity Ir3
 7.9903
 7.9807
 7.9710
 7.9614
 7.9518



In your solution, derive the contribution of the different reference samples in the radioactive signature of each subject. Analyze the conditioning and which contributions are relevant proof of a connection and which might be due to numerical errors. hint

Exc 3: Solve Heath Computer problem 3.5 a,b (page 153-154, hint)