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Math 148 Quiz 6: §9.2-9.4
Directions: Answer each question completely.
credit, and circle your final answer.
Show all work to receive full
1. Assume that the population is divided into three age classes and that 20% of the
females of age 0 and 70% of the females of age 1 survive until the end of the next
breeding season. Assume further that females of age 1 have an average of 3.2 female
offspring and females of age 2 have an average of 1.7 female offspring. If the initial
population consists of 2000 females of age 0, 800 females of age 1, and 200 females of
age 2, find the Leslie matrix and the age distribution at time t = 1.
1
2. Consider the Leslie matrix

1 2.5 3 1.5
0.9 0
0
0

L=
 0 0.3 0
0
0
0 0.2 0

Determine the average number of female offspring of a two-year-old female. (Circle
your answer choice).
(a) 1
(b) 2.5
(c) 3
(d) 1.5
(e) 0
3. Find the components of the vector ~x that has magnitude 4 and is 140◦ counterclockwise
from the positive x-axis.
−→
4. Let A = (0, 1, −3) and B = (−1, −1, 2). Find a unit vector in the direction of AB.
2