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Math Help - Exponential decay with a twist

  1. #1
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    Arziona
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    Exponential decay with a twist

    Oh, please help! What equation would you use to solve this story problem.

    There are 3,000 birds. The population declines by 20% every year. BUT 400 new birds are added every year. How many birds will ther be at the end of seven years?

    Thank you so much!
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  2. #2
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    Re: Exponential decay with a twist

    I'd rather do it like this, but perhaps you're looking for something more fancier. Just a thought.

    Amount of birds after
    1. year: x(1) = 0,8*3000 + 400
    2. year: x(2) = 0,8(0,8*3000 + 400) + 400
    = 0,82 *3000 + 0,8*400 +400
    .
    .
    7th year: x(7) = 0,87 *3000 + 0,86 *400 + ... + 400
    = 0,87 *3000 + 400*(1-0,86)/(1-0,8) , sum of a geometric series
    = 2104,8576
    2100 , or how ever you round it
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