LS 30A - Final Exam with correct answers

Final Exam Last Name: First Name: Student ID: Signature: Instructions: Do not open this exam until instructed to do so. You will have three hours to complete the exam. Please print your name and student ID number above. You may not use books, notes, or any other material to help you. You will need a calculator for some problems. Please make sure your phone is silenced and stowed where you cannot see it. You may use any available space on the exam for scratch work. If you need more scratch paper, please ask one of the proctors. Please do not write below this line. Problem Max Score 1 10 2 8 3 14 4 18 5 20 6 20 7 12 8 8 Total 110 1. (10 pts) Meerkats rely on each other to raise their young. Use the following assumptions to model the number of adult meerkats, M, in a population. You can invent parameters as necessary and, if you don’t remember the formula for a function, sketch it for partial credit. • The per-capita rate at which meerkats give birth to babies who survive to adulthood is a steep sigmoid function of the adult population, with higher reproductive success at higher populations. • Meerkats die of natural causes at a constant per-capita rate d. • Meerkats are preyed upon by eagles and jackals. These predators have many other prey, so their population does not depend on the meerkat population. • The rate at which jackals prey on meerkats is a non-sigmoid saturating function of the meerkat population. • The rate at which eagles prey on meerkats is a sigmoid function of the meerkat population. The sigmo