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Math Help - Difficult exponential equation

  1. #1
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    Difficult exponential equation

    Hi,

    I have two equations... I want to find the minimum number of years when S2>S1

    S1= 0.5n(22000+(n-1)400)
    S2= (10000(1.07^n -1)/(1.07-1))

    I tried really really hard to solve this, but I ended up with some crap where n should be a negative number, which is impossible. The answer must be 6.33, btw)

    I would very much appreciate it if anyone can help me out.

    Thanks in advance
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  2. #2
    Grand Panjandrum
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    Re: Difficult exponential equation

    Quote Originally Posted by IBstudent View Post
    Hi,

    I have two equations... I want to find the minimum number of years when S2>S1

    S1= 0.5n(22000+(n-1)400)
    S2= (10000(1.07^n -1)/(1.07-1))

    I tried really really hard to solve this, but I ended up with some crap where n should be a negative number, which is impossible. The answer must be 6.33, btw)

    I would very much appreciate it if anyone can help me out.

    Thanks in advance
    You will need to solve this either graphically of numerically.

    CB
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  3. #3
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    Re: Difficult exponential equation

    Quote Originally Posted by CaptainBlack View Post
    You will need to solve this either graphically of numerically.

    CB
    Can you please show me how to solve it numerically?
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  4. #4
    Grand Panjandrum
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    Re: Difficult exponential equation

    Quote Originally Posted by IBstudent View Post
    Can you please show me how to solve it numerically?
    You want to find a positive root of the equation:

    S_1(n)-S_2(n)=0

    or:

    f(n)=0.5n[22000+(n-1)400]-\frac{10000(1.07^n -1)}{1.07-1}=0

    This is continuous and f(1)>0 and f(7)<0 so there is at least one root in the interval (1,7).

    Now see here for the general method:



    CB
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  5. #5
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    Re: Difficult exponential equation

    Quote Originally Posted by IBstudent View Post
    Hi,

    I have two equations... I want to find the minimum number of years when S2>S1

    S1= 0.5n(22000+(n-1)400)
    S2= (10000(1.07^n -1)/(1.07-

    I tried really really hard to solve this, but I ended up with some crap where n should be a negative number, which is impossible. The answer must be 6.33, btw)

    I would very much appreciate it if anyone can help me out.

    Thanks in advance

    In equationS2 is itt 1.07^(n-1) or 1.07^(n) -1
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