Note: You will receive zero credit if you use built-in functions to compute the

Question

Note: You will receive zero credit if you use built-in functions to compute the solution to this problem.

You are allowed to call any functions you wrote previously in the class, but you must include them

when you turn in your finished assignment .

The local population of an insect species P(t) can be given using a simple population model

where r is the daily birth rate of the insect species, I is the amount of insects that immigrate to

the area daily, E is the daily emigration rate, b is the number of insects consumed every day by

birds as food, and d is the number of insects that die daily from other causes (i.e. getting run over

by windshields and other natural causes).

From previous studies, you know that the birth rate r = 0.05 daily births per insect; also, every

day 130 insects immigrate from neighboring regions, 100 leave the region, 12 insects become bird

snack, and 25 die from other causes.

(a) Using a Forward Euler finite-difference approximation and a time resolution (delta)t = 1 week,

answer the following questions:

i. If there are initially 100 insects in the area will the population survive? If not, when do

they die out?

(b) Repeat part a) with a time resolution (delta)t = 1 day.

(c) Plot the population P(t) as a function of time for parts a) and b) on the same graph. Are there

any differences in the population trends? Why?

(d) Repeat parts a-c) with an initial insect population of 120 insects. Discuss your observations.

You can also use t_max = 10 weeks to help you solve the problem.

Please send me a working matlab file that is completely finished product. Thanks a lot.

Explanation / Answer

A) they will not survive as all of them will die by the end of FIFTH WEEK (during the fifth week)

clc;

r=0.05;

I=130;

E=100;

b=12;

d=25;

p_0=100;

p_k=p_0;

t_max=70; %n 10*7

h=7; %delta

gen=0; %generations

for i=7:7:t_max

if p_k>=0;

p_k1=p_k*(1+h*r)+h*(I-E-(b+d));

p_k=p_k1;

gen=gen+1;

end

end

B) they will not survive as all of them will die by the end of 26th day

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.