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Math Help - doubling

  1. #1
    Newbie
    Joined
    May 2007
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    doubling

    please help me with this maths question

    moores law states that the number of transistors on an intergrated circuit will double every 18 months can be expressed as

    P = Po * 2t/18

    wher Po is the number of transistors on a circuit and P is the number of transistors t months after the Po

    if the number on a intergrated circuit was 4000 in 1971
    calculate:

    (i)the number of transitors in 1980
    (ii)when did the numbers of transitors break the 1,000,000 mark?

    thank you for any help

    p.s i already think i know how to do this but i cant be 100% sure
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, red55!

    Moore's law states that the number of transistors on an integrated circuit
    will double every 18 months can be expressed as: .P .= .P
    o·2^{t/18}
    where P
    o is the number of transistors on a circuit
    and P is the number of transistors t months after the P
    o.

    If the number on a integrated circuit was 4000 in 1971, calculate:

    (a) The number of transitors in 1980
    (b) When did the numbers of transitors break the 1,000,000 mark?
    In 1971 (t = 0), Po = 4000
    . . Hence, the function is: .P .= .4000·2^{t/18}


    (a) From 1971 to 1980 is 9 years = 108 months.

    Therefore: .P .= .4000·2^{108/18} .= .4000·2^6 .= .256,000


    (b) When was P = 1,000,000 ?

    We have: .4000·2^{t/18} .= .1,000,000

    Divide by 4000: .2^{t/18} .= .250

    Take logs: .ln[2^{t/18}] .= .ln(250)

    Then: .(t/18)·ln(2) .= .ln(250)

    Hence: . t .= .18·ln(250)/ln(2) .= .143.384117 months . .12 years


    Therefore, the 1,000,000 mark was reached in 1983.

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  3. #3
    Newbie
    Joined
    May 2007
    Posts
    10
    thanks for the help
    much appreciated
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