Math 464, Graded Assignment 2
Notes on Exposition:
1. Write clearly and organize your work cleanly.
2. All graphs must be on graph paper or computer generated. All axes must be properly labeled
with units and descriptive names or variables.
3. If you use Excel or other software to generate data, turn in all the data.
4. You might want to write up the entire assignment as an Excel workbook. If so, I encourage
Part I.
Suppose that in a population of Nanimals we have the
following conditions (as represented in the diagram at
right.)
•Birth rate is b= 0.07 per day per animal.
•Death rate is d=N
1000 per day per animal.
•h= 1 animal per day is removed from the popula-
tion.
bN
d
h
1. (10 pts.) Write a difference equation for N.
2. (10 pts.) Find all equilibrium solutions.
3. (10 pts.)
(a) Go to my website. Download the file under the link Random Numbers. (If you can’t
open Excel files, there is a second link for Text Only. If this doesn’t work, email me.)
(b) Under your name you will find two columns of 500 random numbers. These are dis-
tributed normally, with mean and standard deviation 1.
(c) Assume that N(0) = 50. Use your two columns of random numbers to compute three
new columns of data: number of births on each day; numbers of deaths on each day; and
N(t) on each day. Use the first column of random numbers for births and the second for
deaths. For both, use the normal approximation to the binomial distribution.
1
