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Name(s): Score: Math 148 Lab Assignment 6: §9.2-9.4 Directions: You may work in groups of 2–3 to complete this assignment. Answer each question completely. Show all work to receive full credit, and circle your final answer. 1. Assume that a population is divided into three age classes and that 75% of the females of age zero and 30% of the females of age one survive until the end of the next breeding season. Moreover, assume that females of age zero have an average of 1 female offspring, females of age one have an average of 4 female offspring, and females of age two have an average of 2 female offspring. If the initial population consists of 100 females of age zero, 200 females of age one, and 100 females of age two, find the age distribution at time t = 1. 1 2. Consider the Leslie matrix 2 5 8 0.4 0 0 L= 0 0.9 0 0 0 0.8 1 0 0 0 (a) Determine the number of age classes in the population. (b) Determine the fraction of two-year-olds that survive until the end of the next breeding season. (c) Determine the average number of female offspring of a one-year-old female. −→ 3. Let A = (1, 2, 3) and B = (−1, 3, −6). Find a unit vector in the direction of AB. 2 4. Let ~v = h−3, −1i and w ~ = h1, 2i. (a) Find ~v + 2w. ~ Graph the position vectors for ~v and 2w ~ and illustrate ~v + 2w ~ graphically. (b) Find ~v − w. ~ Graph the position vectors for ~v and −w ~ and illustrate ~v − w ~ graphically. 3 5. A triangle has vertices at A = (2, 1, 5), B = (−1, −3, 7), and C = (2, −4, 1). Find the angle at the vertex B. 6. Find the components of the vector ~x that has magnitude 5 and forms and angle of 240◦ measured counterclockwise from the positive x-axis. 4