Worded problems (difference equations)

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August 23rd 2010, 01:12 PM
Mr Rayon

Worded problems (difference equations)

There are 30 000 zebras in Horadina. The number of zebras decreases by 4% each year due to poaching. Each year 5 000 zebras are born, but 1 500 die in infancy.
Write a difference equation to describe this, stating clearly the terms you use.

Any help would be appreciated!
Is the answer Sn+1 = 1.04(Sn) + 3640, S0= 30 000, N=1,2,3...?
August 23rd 2010, 02:46 PM
pickslides

Quote:

Originally Posted by Mr Rayon

decreases by 4%

Therefore $0.96 \times S_0+\dots$

How did you arrive at 3640?
August 23rd 2010, 06:31 PM
Soroban

Hello, Mr Rayon!

pickslides is correct.

Quote:

There are 30,000 zebras in Horadina.
The number of zebras decreases by 4% each year due to poaching.
Each year 5,000 zebras are born, but 1,500 die in infancy.
Write a difference equation to describe this, stating clearly the terms you use.

The population decreases by 4% each year.
Hence, each year, there is only 96% of the preceding population.

And each year, $5,\!000 - 1,\!500 \,=\,3,500$ surviving baby zebras are added.

Therefore: . $S_{n+1} \;=\;0.96S_n + 3500,\;\;S_0 = 30,\!000$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The closed form is: . $S(n) \;=\;87,\!500 - 57,\!500(0.96)^n$
August 24th 2010, 02:00 AM
Mr Rayon

As expected. The answers in the back of my worksheets are WRONG!(Surprised)