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Math Help - Problem with exponential function and logs

  1. #1
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    Problem with exponential function and logs

    Hey, I have run aground on what im sure is a fairly simple logarithmic problem. Any help would be appreciated.
    How would I go about solving a combination exponential and logarithmic problem such as this one:

    Population of a city is observed as growing according to function P(t) = p0e^kt where the population has doubled after the first 30 years

    - Find k
    - By what factor will original population have grown after 120 years...

    I thought to find k it was an application of ln. But im not sure what numbers i should be substituting into the exponential formula and where.
    Please help!
    Thanks
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  2. #2
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    Hi thinkpol , welcome to MHF.
    Population doubles in 30 years. So
    P/Po = 2 = e^kt
    Take log on both sides.
    ln2 = 30*k.
    Using calculator find ln2 and hence find k.
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  3. #3
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    sa-ri-ga-ma

    Im confused

    so after i take:

    ln2 = 30*k

    do i simply divide ie

    ln2/30 = k

    ?

    Thanks for all the help
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  4. #4
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    Is the correct value for k 0.023?

    Quote Originally Posted by thinkpol View Post
    sa-ri-ga-ma

    Im confused

    so after i take:

    ln2 = 30*k

    do i simply divide ie

    ln2/30 = k

    ?

    Thanks for all the help
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
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    Your value is correct.
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