hey my friend, im back, you helped me with my GPS matlab homework...

hey my friend, im back, you helped me with my GPS matlab homework the last time. I know you are pretty good with matlab. are you familiar simbiology? I need help with 3a and 3b of this homework. will tip good on each question. thanks

North Carolina State University Department of Mathematics
Introduction to Applied Mathematics
MA 325 Assignment #1
DUE Date: March 2, 2015
1. A family of salmon fish living off the Alaskan Coast obeys the Malthusian law of population
growth dp ( t ) /dt = 0 . 003 p ( t ), where t is measured in minutes. It is also assumed that at time
t = 0 there are one million salmon.
(a) Using SimBiology , simulate the salmon population, p ( t ).
(b) Now, assuming that at time t = 0 a group of sharks establishes residence in these waters
and begins attacking the salmon. The rate at which salmon are killed by the sharks is
0 . 001 p
2
( t ), where p ( t ) is the population of salmon at time t . Moreover, since an undesirable
element (the sharks) has moved into their neighborhood, 0 . 002 salmon per minute leave
the Alaska waters.
i. Modify the Malthusian law of population growth to take these two factors into ac-
count. Using SimBiology to simulate the salmon population, p ( t ). What happens as
t → ∞ ?
ii. Show that the above model is not realistic. Hint: Show, according to this model, the
salmon population decreases from one million to about one thousand very quickly (in
about one minute).
2. The population of New York City would satisfy the logistic law
dp
dt
=
1
25
p -
1
25 × 10 6
p
2
,
where t is measured in years, if we neglected the high emigration and homicide rates. Assume
that population of New York City was 8 , 000 , 000 in 1970.
(a) Using SimBiology , find the population, p ( t ). What happens as t → ∞ ?
(b) Modify the logistic equation to take into account the fact that 9 , 000 people per year
move from the city, and 1 , 000 people per year are murdered. Using SimBiology , find the
population, p ( t ). What happens as t → ∞ ?
3. Consider a predator-prey model of foxes and rabbits. If we let R ( t ) and F ( t ) denote the number
of rabbits and foxes, respectively, then the Lotka-Volterra model is:
dR
dt
= a * R - b * R * F
dF
dt
= c * R * F - d * F,
where a = 0 . 04, b = 0 . 0005, c = 0 . 00005, and d = 0 . 2.