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Solving for the value for t

  1. Jul 9, 2013 #1
    1. The problem statement, all variables and given/known data

    What value of t will make the function = 250?

    N(t) = 500 / (1+9e^(-5t))
    250 = 500 / (1+9e^(-5t))

    3. The attempt at a solution

    1 + 9e^-5t = 2
    9e^-5t = 1
    t = log1/log(-5)(9e)
    t = 0

    However t = 0 is incorrect because when it is subbed back into the original equation it does not result in 250. How do I solve for the correct value of t?
     
  2. jcsd
  3. Jul 9, 2013 #2
    Your solution is difficult to follow. Everything up to your second step checks out, but I can't understand how you went from the second equation to the third. The third equation also seems completely senseless. You can't take the natural logarithm of a negative number in the real number line.

    If you show your full transition from the second step to the third, we might be able to help you better. But a wild guess from my head suggests that you are somehow misreading the second equation, so I will write it down nicely: [itex] 9e^{-5t} = 1[/itex]. Did that help?
     
  4. Jul 9, 2013 #3

    SteamKing

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    Your are correct to this point:

    9e^(-5t) = 1

    You didn't apply logarithms correctly after this. Here is how to proceed correctly:

    e^(-5t) = 1/9
    Mod note: Deleted the remainder of this post, as it was probably too much help.
    Now take the natural log of both sides:
     
    Last edited by a moderator: Jul 10, 2013
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