Differential Equations Solutions 3

Differential Equations Solutions 3 - . The confdence...

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13 0 5 10 15 20 25 30 35 40 45 50 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Solutions to the differential equation t y Figure 2.3. Results of Challenge 2.4. The black curves result from setting a =0 . 006 and a =0 . 009 . The blue curves have random rates chosen for each year. The red curves are the results of trials with the random rates ordered with largest to smallest. For the green curves, the rates were ordered smallest to largest. where a ( τ ) is the growth rate in year τ . Since exponentials commute, the fnal population is invariant with respect to the ordering oF the rates, but the intermediate population (and thus the demand For social services and other resources) is quite di±erent under the two assumptions. CHALLENGE 2.5. The solution is given in exlinsys.m
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Unformatted text preview: . The confdence intervals For the frst example are x 1 [ 1 . 0228 , 1 . 0017] , x 2 [1 . 0018 , 1 . 0022] and For the second example are x 1 [0 . 965 , 1 . 035] , x 2 [ 1 . 035 , . 965] . Those For the second example are 20 times larger than For the frst, since they are related to the size oF A 1 , but in both cases about 95% oF the samples lie within the intervals, as expected. Remember that these intervals should be calculated using a Cholesky decom-position or the backslash operator. Using inv or raising a matrix to the 1 power is slower when n is large, and generally is less accurate, as discussed in Chapter 5....
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