 
Summary: SIMS Program 2010, Math 3B/3C Worksheet 3
Grace Kennedy, Friday August 20th
SIMS Website: http://www.epsem.ucsb.edu/summer programs/sims.html
Course Website: http://math.ucsb.edu/kgracekennedy/SIMSsummer2010.html
NAME:
Group Mates:
1. (Longterm Behavior) Let y(t) (read "y of t") be the snowy plover pop
ulation around Santa Barbara t years after the 1973 Endangered Species
Act, in which they are listed an endangered species.1
(a) If the change in the snowy plover population is proportional to the
current population, what is the differential equation that models their
growth? (Let k denote your constant of proportionality.)
(b) What will the longterm behavior (i.e. will snowy plovers take over
Earth, become extinct, or coexist peacefully with other terrestrial
beings in billion years) be in each of the following cases?
i. k > 0
ii. k = 0
iii. k < 0
2. (Logistic Model) It is unlikely that the snowy plover population follows
such a simple model. Suppose now that the growth rate of the snowy
