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# f03t1 - Math 224 Test 1 Fall 2003 Oct.2 David Gurarie Name...

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Math. 224. Test 1 Fall 2003. Oct.2 David Gurarie Name 1. Modeling. Set up di ff erential equation models of the following systems. Classify them (DE/DS, fi rst or higher order, linear/nonlinear, autonomous, separable, etc.). Indicate solution method(s) for each one (analytic, numeric), but do not solve . (a) The logistic growth model with the growth rate k , carrying capacity N = 6, initial population y 0 , and harvesting rate b ( t ). Which b allow analytic solutions? (b) Mixing problem with incoming rate r 1 = 3 m 3 /s , concentration α 1 = . 1 mg/m 3 , outgoing rate r 2 = 2 m 3 /s , and initial volume V 0 = 20 m 3 Problem Score 1(25) 2(25) 3(25) 4(25) Total

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(c) Financing loan model with interest rate α , and payment rate p . Write solutions, and sketch solution curves. Extra : explain the minimal payment rate, fi nd total payment and the overpay factor. (d) Oscillator (mass-spring) system of mass m , friction coe cient α , spring constant k , suspended vertically in the external gravity force mg Write it as a single equa- tion, and convert to a di ff erential system.
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f03t1 - Math 224 Test 1 Fall 2003 Oct.2 David Gurarie Name...

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