SIMS Program 2010, Math 3B/3C Worksheet 3 Grace Kennedy, Friday August 20th 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. (Long-term 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 long-term 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 Collections: Mathematics