MATH 190 - Mathematical Models of Population Growth
Due by 5 p.m. Friday, November 9, 2007
Name:
1. The following table lists reproduction and survival rates for the female population of possum in the
United States. Suppose possums give birth only once a year, which dictates a natural time step of
one year. Due to natural life span and traffic possums seldom if ever live longer than 5 years, which
gives a natural stopping point for the age classes.
Birth and Survival Rates for Female Possums
Age (years) Birth Rate Survival Rate
0 - 1 0.0 0.6
1 - 2 1.3 0.8
2 - 3 1.8 0.8
3 - 4 0.9 0.4
4 - 5 0.2 0.0
Let Arepresent the number of possums in the 0-1 year age group; Bthe number of possums in the
1-2 year age group; Cthe number of possums in the 2 - 3 year age group; Dthe number of possums
in the 3 - 4 year age group; and Dbe the number of possums in the 4 - 5 year age group.
(a) [20 points] Fill in the values on the state diagram that models this situation. Make sure to label
your components neatly and put your name on the paper.
(b) [30 points] Using MATLAB, calculate the number of female possums in each age group and in
total for the years indicated below and fill those values in the appropriate columns of the chart.
Round your answer to the ONE DECIMAL PLACE.
Age Initial After After After After After
Group Year 1 Year 2 Years 11 Years 12 Years 13 Years
A(0 - 1) 194
B(1 - 2) 82
C(2 - 3) 55
D(3 - 4) 22
E(4 - 5) 6
Total
Female 359
Population
