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Math Help - find a general formula for N reductions

  1. #1
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    find a general formula for N reductions

    Hi,

    I want to find what will be left of number X, after 50 reductions of 2% - each time the reference is whats left from the total sum.

    I was trying to find a general formula for this but without success.


    x - 0.02X - 0.02(x-0.02x) - 0.02(x - 0.02X - 0.02(x-0.02x)) - ..... (N times)


    please help me find a formula for N reductions.
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  2. #2
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    Re: find a general formula for N reductions

    Quote Originally Posted by sergeyrar123 View Post
    Hi,

    I want to find what will be left of number X, after 50 reductions of 2% - each time the reference is whats left from the total sum.

    I was trying to find a general formula for this but without success.


    x - 0.02X - 0.02(x-0.02x) - 0.02(x - 0.02X - 0.02(x-0.02x)) - ..... (N times)


    please help me find a formula for N reductions.
    1. If you reduce a value by 2% then there is left 98% of the original value.

    2. With your example:

    N=1 : V = 50 - 50 \cdot \frac2{100} = 50 \cdot \frac{98}{100}

    N=2 : V = 50 \cdot \frac{98}{100} - 50 \cdot \frac{98}{100} \cdot \frac2{100} = 50 \cdot \frac{98}{100}\cdot \frac{98}{100} = 50 \cdot \left(\frac{98}{100}\right)^2

    N=3 : V = 50 \cdot \left(\frac{98}{100}\right)^2 - 50 \cdot \left(\frac{98}{100}\right)^2 \cdot \frac2{100} = 50 \cdot \left(\frac{98}{100}\right)^2\cdot \frac{98}{100} = 50 \cdot \left(\frac{98}{100}\right)^3


    ... and so on. I guess you see that the 50th reduction of 50 is calculated by:

    V = 50 \cdot (0.98)^{50} \approx 18.21
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  3. #3
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    Re: find a general formula for N reductions

    YES !!
    Thanks alot!
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