#OK to post homework
#Nicholas DiMarzio, 09/06/21, Assignment 1
#
#Problem 2
#R(n):The number of females born at time n
#
#Assumptions: R(0)=c0, R(1)=c1, R(2)=c2
#
R := proc(n, p1, p2, p3, c0, c1, c2) option remember;
if n = 0 then
c0;
elif n = 1 then
c1:
elif n = 2 then
c2:
else
expand(p1*R(n - 1, p1, p2, p3, c0, c1, c2) + p2*R(n - 2, p1, p2, p3, c0, c1, c2) + p3*R(n - 3, p1, p2, p3, c0, c1, c2)): #Recurrence
fi:
end:

#Problem 3
#Using the proc in problem two I called the proc using n=1000
#keeping c0,c1,c2 as 1 I changed p1,p2,p3 to different values to find out when there was extinction, stable population, and population explosion.
#
#part i - extinction

(R(1000,0.01,0.01,0.01,1,1,1));

#This returns an exremely small number which would represent extinction

#part ii - stable population

(R(900,1/3,1/3,1/3,1,1,1));

=1

(R(1000,1/3,1/3,1/3,1,1,1));

=1

(R(1100,1/3,1/3,1/3,1,1,1));

=1

#Therefore this population is stable for p1,p2,p3 = 1/3

#part iii - population explosion

(R(1000,1,1,1,1,1,1));

#This returns and extremely large number which represents a population explosion