Math 155-004, Quiz 4 February 17, 2009 NAME:

Math 155-004, Quiz 4
February 17, 2009
Instructions: This quiz is closed books and closed notes. You may use calculators. Work that is erased or
crossed out will not be graded.
1. (7 pts) Let Vt represent the voltage of the AV node in the Heart Model.
Vt + u if Vt ≤ eατ Vc
Vt+1 =
if Vt > eατ Vc
Let e−ατ = 51 , u = 10, and Vc = 2.
a) If V0 = 6, calculate V1 . Will the heart beat? Why or why not?
b) Does this system have an equilibrium? If so, find it algebraically; if not, explain why not.
c) Graph the updating function and cobweb from an initial value of V0 = 6 to determine if this heart is
i) healthy, ii) has a 2:1 block, or iii) has the Wenckebach phenomenon.
2. (3 pts) Graphed below is an updating function f (mt ), along with the diagonal. Cobweb starting from
an initial value of 0.6. Is the equilibrium m∗ = 1 stable or unstable?
Extra Credit: In the article, R(t) refers to the love (or hate if negative) of
(someone’s name).