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COBWED IS BY GOOGLE DRIVE MATH 3050 Mathematics and Biology
Homework 1
1. It is known that a given population triples each hour, due to the net effect of fecundity and deaths.
Show the equations that model the population, in each of the two formalisms:
(a) provide a formula for P+ in terms of P;
(b) provide a formula for ∆P in terms of P;
2. Consider the model ∆P = 0.8P(1 −P/10).
(a) Plot ∆P as a function of P manually.
(b) Construct a table of values of Pt for t = 0,1,2,3,4,5 starting from P0 = 1.
(c) Construct a cobweb beginning at P0 = 1 and compare the values from cobweb to those you
obtained in the table.
(d) Plot P(t) as a function of t. (Construct an iteration map)
3. Consider the difference equation:
xn+1 = rxn(1 −xn),x0 = 0.1
(a) Plot the first 30 terms of the solution to the difference equation with r = 0.9,1.5,3,4.
(b) Draw the cobweb maps for each case above.
