# quiz 4 - Math 155 Quiz 4 Name SOLUTIONS Also put your name...

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Math 155 Quiz 4 September 19, 2006 Name: SOLUTIONS Also put your name on the back. Calculators are allowed on this quiz. Remember to show all work to receive full credit. 1. Let p t +1 = 1 . 2 p t 1 . 2 p t + 1 . 3(1 - p t ) a) What are the equilibria? (Hint: you do not need to justify your answer.) The equilibria are always 0 and 1 for this system. b) What is the long term behavior of this updating function? Why? 1.2 describes mutant reproduction while 1.3 describes wild type reproduction. Since the wild type bacteria are reproducing faster, the population will become 100% wild.
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Unformatted text preview: OR mutants will die out. OR p t → 2. Consider the following discrete time dynamical system of a heart model, with α = 1 . 0, τ = 1 . 0, V c = 20, and u = 10. V t +1 = ± e-ατ V t + u if V t ≤ e ατ V c e-ατ V t if V t > e ατ V c ± If V = 30, will the heart beat? Show why. The heart beats because: 30 < e (1 · 1) 20 = 54 . 37 or e (-1 · 1) (30) = 11 . 036 < 20 ± What is the equilibrium? Show your work. V * = e-1 V * + 10 V *-e-1 V * = 10 V * (1-e-1 ) = 10 V * = 10 1-e-1 = 15 . 819767...
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