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    A fishing lake is initially stocked with 1000 fish.


    It is estimated that each year 20% of the fish are caught or die.
    At the end of each year the lake is restocked with 100 fish.


    (i) Calculate the estimated number of fish in the lake at the end of Year 1, Year 2
    and Year 3 [3]


    These numbers are the first 3 terms of a sequence.


    (ii) Find a recurrence relation for this sequence. [2]

    Okay so, I got 900,820 and 756 for part (i)


    (iii) Find the limit to which this sequence converges. [2]

    I have highlighted in bold what I can't do, would someone mind helping me out? thanks
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    (Original post by upthegunners)
    A fishing lake is initially stocked with 1000 fish.


    It is estimated that each year 20% of the fish are caught or die.
    At the end of each year the lake is restocked with 100 fish.


    (i) Calculate the estimated number of fish in the lake at the end of Year 1, Year 2
    and Year 3 [3]


    These numbers are the first 3 terms of a sequence.


    (ii) Find a recurrence relation for this sequence. [2]

    Okay so, I got 900,820 and 756 for part (i)


    (iii) Find the limit to which this sequence converges. [2]

    I have highlighted in bold what I can't do, would someone mind helping me out? thanks

    Ok, so your numbers are correct

    Do you know what it means by "recurrence relation"

    If so you should just be able to write it down as you have performed the operation on 1000, 900, and 820
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    (Original post by TenOfThem)
    Ok, so your numbers are correct

    Do you know what it means by "recurrence relation"

    If so you should just be able to write it down as you have performed the operation on 1000, 900, and 820
    0.8 * u + 100 ??
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    (Original post by upthegunners)
    0.8 * u + 100 ??
    You need to write it as a recurrence relationship

    u_{n+1} =
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    (Original post by TenOfThem)
    You need to write it as a recurrence relationship

    u_{n=1} =
    why do we have to write it as this?
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    (Original post by upthegunners)
    why do we have to write it as this?
    It should be u_{n+1}= ... - the equals sign was just a mistake.
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    (Original post by Mr M)
    It should be u_{n+1}= ... - the equals sign was just a mistake.
    TA
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    (Original post by upthegunners)
    A fishing lake is initially stocked with 1000 fish.


    It is estimated that each year 20% of the fish are caught or die.
    At the end of each year the lake is restocked with 100 fish.


    (i) Calculate the estimated number of fish in the lake at the end of Year 1, Year 2
    and Year 3 [3]


    These numbers are the first 3 terms of a sequence.
    For the limit


    (ii) Find a recurrence relation for this sequence. [2]

    Okay so, I got 900,820 and 756 for part (i)


    (iii) Find the limit to which this sequence converges. [2]

    I have highlighted in bold what I can't do, would someone mind helping me out? thanks
    You have a recurrence relation of u_{n+1}=0.8u_n+100
    Let the limit be A, then
    u_{n+1}->A and u_n->A
    So
    A=0.8A+100
    Solve A
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    (Original post by upthegunners)
    A fishing lake is initially stocked with 1000 fish.


    It is estimated that each year 20% of the fish are caught or die.
    At the end of each year the lake is restocked with 100 fish.


    (i) Calculate the estimated number of fish in the lake at the end of Year 1, Year 2
    and Year 3 [3]


    These numbers are the first 3 terms of a sequence.
    For the limit


    (ii) Find a recurrence relation for this sequence. [2]

    Okay so, I got 900,820 and 756 for part (i)


    (iii) Find the limit to which this sequence converges. [2]

    I have highlighted in bold what I can't do, would someone mind helping me out? thanks
    For the limit:

    You have a recurrence relation of u_{n+1}=0.8u_n+100
    Let the limit be A, then
    u_{n+1}->A and u_n->A
    So
    A=0.8A+100
    Solve A
 
 
 
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