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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: Nomvalt on August 24, 2010, 07:29:18 am

Title: IS THIS RIGHT? (difference equations)
Post by: Nomvalt on August 24, 2010, 07:29:18 am

There are 30 000 zebras in Horadina. The number of zebras decreases by 4% each year due to poaching.
Each year 5000 zebras are born, but 1500 die in infancy.
Write a difference equation to describe this, stating clearly the terms you use.

Letting Z_n = number of zebras in Horadina at the end of the nth year and Z₀ = 30 000.
Is the correct answer:

In general, Z_n+1 = 1.04(Z_n + 3500), 
Z_n+1 = 1.04 Z_n + 3640, Z₀ = 30 000, n = 1, 2, 3,...

?   

Title: Re: IS THIS RIGHT? (difference equations)
Post by: ChairmanMao on August 24, 2010, 07:50:04 am

No, it's decreasing, so it can't be 1.04
ZN+1 = 0.96Zn + 3500, Z0= 30000
OR
Zn = 0.96Zn-1 + 3500, Z0= 30000

"Zn+1 = 1.04 Zn + 3640, Z0 = 30 000, n = 1, 2, 3,..." Where did you get 3640 from?

Title: Re: IS THIS RIGHT? (difference equations)
Post by: Nomvalt on August 24, 2010, 08:30:22 am

Quote from: ChairmanMao on August 24, 2010, 07:50:04 am

No, it's decreasing, so it can't be 1.04
ZN+1 = 0.96Zn + 3500, Z0= 30000
OR
Zn = 0.96Zn-1 + 3500, Z0= 30000

"Zn+1 = 1.04 Zn + 3640, Z0 = 30 000, n = 1, 2, 3,..." Where did you get 3640 from?

It was in the answers to a practice sac. had a feeling it was wrong. thanks.