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Math Help - Worded problems (difference equations)

  1. #1
    Member Mr Rayon's Avatar
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    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...?
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Quote Originally Posted by Mr Rayon View Post
    decreases by 4%
    Therefore 0.96 \times S_0+\dots

    How did you arrive at 3640?
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  3. #3
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    Hello, Mr Rayon!

    pickslides is correct.


    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
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  4. #4
    Member Mr Rayon's Avatar
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    As expected. The answers in the back of my worksheets are WRONG!
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