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- anonymous

any help with difference equations?

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- anonymous

any help with difference equations?

- jamiebookeater

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- anonymous

Sure!
http://docs.google.com/viewer?url=http://www2.fiu.edu/~thompsop/modeling/modeling_chapter3.pdf

- anonymous

couldnt open the file

- anonymous

http://www2.fiu.edu/~thompsop/modeling/modeling_chapter3.pdf

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- anonymous

ty

- anonymous

could I send you a problem that I need help with?

- anonymous

Ive been working on the same problem for two hours.

- anonymous

Okay, sure!

- anonymous

ok. Let me type it in real quick.
Suppose a region has 8000 healthly elm trees. In 1950, bark beetles harboring the fungus arrive in the region. In each subsequent year, the number of elm trees that contract the disease is 20% of the number of healthy trees at the end of the previous year. Once the tree is infected, it stars infected. Find the difference equation describing the spread of Dutch elm disease through the regions 8000 elm trees.

- anonymous

(a) Since there are 8000 trees and 20% chance of being infected, the number of healthy trees would be 80% of the trees that were healthy the year before. Thus, the equation is
f(x) = 8000(1-0.8^x) where x is the years that have passed and f(x) is the number of sick trees.
As can be seen, after only 3 years almost half of the trees are infected.
(b)
0 8000
1 6400
2 5120
3 4096
4 3276.8
5 2621.44
Now these should really be in integers, so year 4 is 3277, which makes 5 into 2621.6,
which rounds up to 2622.
(c) Make a graph, with the x-axis as years and the y-axis as the number of trees.
(d) Already solved it.
(e) I did the first column by rounding each time and the second by using numbers past the decimal. As can be seen, there is little difference between them.
Year Uninfected Trees
1 0 0
2 1600 1600
3 2880 2880
4 3904 3904
5 4723 4723.20
6 5378 5378.56
7 5902 5902.85
8 6322 6322.28
9 6658 6657.82
10 6926 6926.26
11 7141 7141.01
12 7313 7312.81
13 7450 7450.24
14 7560 7560.20
15 7648 7648.16
16 7718 7718.53
17 7774 7774.82
18 7819 7819.86
19 7855 7855.88
20 7884 7884.71
(f) As can be seen, 7560 is in the column above; the year is the number of the left.

- anonymous

Thank you, how did you know there was a b,c,d,e and f to that problem?

- anonymous

Google can be a savior sometimes...
http://en.allexperts.com/q/Algebra-2061/2010/5/question-5.htm
Just don't limit yourself, try to explore. I'm glad you're trying hard though. Just keep doing what you're doing and if you can't still find the answer, just sign in here and ask questions. But I'd like to see guys like you also post what they tried and didn't work, etc. Just to kind of prove that you're trying and not waiting to have everything done for you.
Great job, and keep working hard. We'll be around the help out when needed. ;)

- anonymous

Thank you and can I post what I was doing here?

- anonymous

I had yn=80yn-1+0 , yo8000

- anonymous

After doing all of the math, I realized that this graph was going to be going down, and if 20% was infected, it would of came out wrong.

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