Further Exam questions help

[nikeets]

Ello errbody!
I've done  the 2008 vcca exam 1. I've made corrections but I don't get qs 8 and 9 from Matrices Module.
Help meh plz
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2008furmath1-w.pdf

[#J.Procrastinator]

Hi there!

Question 8
This transition matrix predicts that, in the long term, the mutton birds will
A. nest only at site A.
B. nest only at site B.
C. nest only at sites A and C.
D. nest only at sites B and D.
E. continue to nest at all four sites.

Use the transition matrix and raise it to any high power such as 100. This will give you the site at which the mutton birds will reside in the long run.
You'll find that only site B and D fit this criteria. Ans: D

Question 9
Six thousand mutton birds nest at site B in 2008.
Assume that an equal number of mutton birds nested at each of the four sites in 2007. The same transition
matrix applies.
The total number of mutton birds that nested on the island in 2007 was
A. 6 000
B. 8 000
C. 12 000
D. 16 000
E. 24 000

Here I would let x= the number of birds nesting at each of the sites. Because 2008 is the next year (after 2007) we use the values for B in the next year (that is, the second column)

6000 birds nested at site B in 2008. Hence, 6000= x+0.15x+0.3x
                                                                     6000= 1.5x
                                                                        x= 4000 (This only gives the number of birds at one site!!)

4000 x 4 (there are four different sites) = 16000

Therefore, answer is D.

Hope this helps! Happy to explain further

[nikeets]

Thank you my saviour! But I don't quite understand the results i get for 8. I put in the transition matrix and raise it to 100, and then I get another matrix. How can I tell from that? Is it just that B and D have all their birds staying and not going anywhere else while the ones starting at A and C will eventually go to B and D and stay there? LOL

[#J.Procrastinator]

Thank you my saviour! But I don't quite understand the results i get for 8. I put in the transition matrix and raise it to 100, and then I get another matrix. How can I tell from that? Is it just that B and D have all their birds staying and not going anywhere else while the ones starting at A and C will eventually go to B and D and stay there? LOL

You're welcome Well if you continue to raise the transition matrix to higher powers like 150 or so, you'll find that the number of birds nesting at Site A and Site C will eventually come to 0, or close to 0. Whereas, Site B and D have all the mutton birds nesting there in the long run.

[nikeets]

Whereas, Site B and D have all the mutton birds nesting there in the long run.

That makes so much sense, because there'll always be bird there. Dat logic. I see the light. Thanks 

[unfamila]

There wont be if you put it to the power of 100000000000000000000000000. However, i don't suggest you do this, my calculator in the internal exam froze for ages when i done this...