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Math Help - Exponential problem

  1. #1
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    Exponential problem

    A exponential curve relating two quantities 'q' and 't' has the form q=ae^kt where a and k are constants.
    The curve passes through two points (0.09036,2) and (3.307,-4)
    Determine the values of 'a' and 'k' and find the value of 't' when q= 1.5

    I have no idea where to even start this one guys could someone help me.
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  2. #2
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    q = a\,e^{k\,t}, and you know that (t, q) = (0.09036, 2) and (t, q) = (3.307, -4) lie on the curve.

    What you have been given in nonsense, as the exponential function never crosses the horizontal axis. So you can't have the values of q being different sign...


    Just to be sure:

    Substituting these points gives two equations in two unknowns:

    2 = a\,e^{0.09036k}

    -4 = a\,e^{3.307k}.


    Dividing Equation 2 by Equation 1 gives:

    \frac{-4}{\phantom{-}2} = \frac{a\,e^{3.307k}}{a\,e^{0.09036k}}

    -2 = e^{3.21664k}.

    This is clearly impossible since the exponential function is always positive.
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    Hi thanks for replying,you say the problem is nonsense but i have worked it to this below,have i not understood the problem ?

    q= ae^kt

    3.307=ae^ -4k

    0.09036=ae^2k

    36.598=e^ -6k

    -6k=ln36.598 = 3.599

    k= 3.599/-6 = -0.599

    3.307=ae^2.396

    a=3.307/e^2.396 = 0.3012

    when q = 1.5

    1.5 = 0.3012e^-0.599t

    1.5/0.3012 = e^-0.599t

    4.98 = e^-0.599t

    -0.599t = ln4.98 = 1.6054

    t= 1.6054/-0.599 = -2.68
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  4. #4
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    Quote Originally Posted by bbeweel View Post
    Hi thanks for replying,you say the problem is nonsense but i have worked it to this below,have i not understood the problem ?

    q= ae^kt

    3.307=ae^ -4k

    0.09036=ae^2k

    36.598=e^ -6k

    -6k=ln36.598 = 3.599

    k= 3.599/-6 = -0.599

    3.307=ae^2.396

    a=3.307/e^2.396 = 0.3012

    when q = 1.5

    1.5 = 0.3012e^-0.599t

    1.5/0.3012 = e^-0.599t

    4.98 = e^-0.599t

    -0.599t = ln4.98 = 1.6054

    t= 1.6054/-0.599 = -2.68
    you have messed up the 'q' and 't' while substituting and how can time be negative?
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    Yes i overlooked time being negative :-/
    I have swapped my 'q' and 't' around and i now have the answers k = 0.600 , a = 0.996 and t = 0.6823 ??? could you please let me know if i am even close here ?
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    Quote Originally Posted by bbeweel View Post
    Yes i overlooked time being negative :-/
    I have swapped my 'q' and 't' around and i now have the answers k = 0.600 , a = 0.996 and t = 0.6823 ??? could you please let me know if i am even close here ?
    why are you swapping dependent and independent variables? did you make a mistake interpreting the original problem statement?

    it would help if you stated the original problem in its entirety.
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    Quote Originally Posted by skeeter View Post
    why are you swapping dependent and independent variables? did you make a mistake interpreting the original problem statement?

    it would help if you stated the original problem in its entirety.
    A exponential curve relating two quantities 'q' and 't' has the form q=ae^kt where a and k are constants.
    The curve passes through two points (0.09036,2) and (3.307,-4)
    Determine the values of 'a' and 'k' and find the value of 't' when q= 1.5

    I have worked it to this so far below:

    q= ae^kt

    3.307=ae^ -4k

    0.09036=ae^2k

    36.598=e^ -6k

    -6k=ln36.598 = 3.599

    k= 3.599/-6 = -0.599

    3.307=ae^2.396

    a=3.307/e^2.396 = 0.3012

    when q = 1.5

    1.5 = 0.3012e^-0.599t

    1.5/0.3012 = e^-0.599t

    4.98 = e^-0.599t

    -0.599t = ln4.98 = 1.6054

    t= 1.6054/-0.599 = -2.68
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  8. #8
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    Quote Originally Posted by bbeweel View Post
    A exponential curve relating two quantities 'q' and 't' has the form q=ae^kt where a and k are constants.
    The curve passes through two points (0.09036,2) and (3.307,-4)
    Determine the values of 'a' and 'k' and find the value of 't' when q= 1.5
    the ordered pair is (t,q)

    as stated earlier, this problem is bogus. the only way to get a negative value for q is for a to be negative ... but then, all values of q would have to be negative.

    if the equation has the form q = ae^{kt} + c , then a solution may exist with the given coordinates.

    btw ... time can be negative, it's just a time prior to when t = 0.


    if the coordinates were swapped, then your solution is close.

    I get k = -0.5999 , a = 0.3000 , and q(1.5) = 0.1220
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