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    The population of a colony of insects increases in such a way that if it is N at the beginning of the week, then at the end of the week it is a+bN, where a and b are constants and 0<b<1. Starting from the beginning of the week when the population is N, write down an expression for the population at the end of 2 weeks. Show that at the end of c consecutive weeks the population is a(1-bc/1-b)+bcN.

    When a=2000 and b=0.2, it is known that the population takes about 4 weeks to increase from N to 2N. Estimate a value for N from this information.
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    (Original post by cucumberpj)
    The population of a colony of insects increases in such a way that if it is N at the beginning of the week, then at the end of the week it is a+bN, where a and b are constants and 0<b<1. Starting from the beginning of the week when the population is N, write down an expression for the population at the end of 2 weeks. Show that at the end of c consecutive weeks the population is a(1-bc/1-b)+bcN.

    When a=2000 and b=0.2, it is known that the population takes about 4 weeks to increase from N to 2N. Estimate a value for N from this information.
    So how far have you got with this?
    Can you show us some working?
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    (Original post by davros)
    So how far have you got with this?
    Can you show us some working?
    I really don't know how to solve it...
    I can't understand the question, it is A.P. or G.P.?
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    (Original post by cucumberpj)
    I really don't know how to solve it...
    I can't understand the question, it is A.P. or G.P.?
    You have been given a formula


    Start of W1 = N

    End of W1 = a+bN

    So start of W2 = a+bN

    So what is end of W2
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    (Original post by TenOfThem)
    You have been given a formula


    Start of W1 = N

    End of W1 = a+bN

    So start of W2 = a+bN

    So what is end of W2
    End of W2 = a+bN+(a+bN-N)= 2a+2bN-N
    Is it correct?
    :confused:
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    (Original post by cucumberpj)
    End of W2 = a+bN+(a+bN-N)= 2a+2bN-N
    Is it correct?
    :confused:
    Where did you get that

    The end of the week = a + b(start of week)
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    (Original post by cucumberpj)
    I really don't know how to solve it...
    I can't understand the question, it is A.P. or G.P.?
    Forget about APs and GPs for the moment and just use the formula as TenOfThem suggests.

    Whatever the start-value is at the beginning of the week, you are told that the end-value at the end of the week is given by the formula

    end-value = a + b x start-value

    So if you start the week with N, you end the week with a + bN.
    So if you start the 2nd week with a + bN, what is the value at the end of the 2nd week?
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    (Original post by davros)
    Forget about APs and GPs for the moment and just use the formula as TenOfThem suggests.

    Whatever the start-value is at the beginning of the week, you are told that the end-value at the end of the week is given by the formula

    end-value = a + b x start-value

    So if you start the week with N, you end the week with a + bN.
    So if you start the 2nd week with a + bN, what is the value at the end of the 2nd week?
    a+b(a+bN)
    i knew how to show it ,but now i don't know how to estimate a value for N.
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    (Original post by cucumberpj)
    a+b(a+bN)
    i knew how to show it ,but now i don't know how to estimate a value for N.
    Have you done the bit about the result after c consecutive weeks?
 
 
 
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