Name(s):
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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.
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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.
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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.
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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.
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