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Math Help - Population Growth

  1. #1
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    Population Growth

    Dear Forum I am having problems with the following any feedback would be appreciated:
    If the population in a particular country is growing at 1.7% compounded continuously, how long will it take the population to double? (Round up to the next higher year if not exact.)


    thanks -AC-
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  2. #2
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    Try

    P=P_0e^{rt}

    where P_0 = initial population, r = growth rate and t = time in years and P= 2\times P_0

    you should find

    2P_0=P_0e^{1.07t}

    2=e^{1.07t}

    ln(2)=1.07t

    t= \frac{ln(2)}{1.07} years
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  3. #3
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    Something fishy going on there. ln(2)/1.07 < 1. It's growing at 1.7% per year and doubles in less than a year?

    Using the classical Rules of 72, we get an approximation of 72 / 1.7 = 42.353 years. Let's find a model that produces a result in this neighborhood.

    2 = 1.017^{t}

    Or, if you insist on e-base.

    2 = e^{ln(1.017)*t} = e^{0.01685712*t}
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  4. #4
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    Quote Originally Posted by pickslides View Post
    Try

    P=P_0e^{rt}

    where P_0 = initial population, r = growth rate and t = time in years and P= 2\times P_0

    you should find

    2P_0=P_0e^{1.07t}

    2=e^{1.07t}

    ln(2)=1.07t

    t= \frac{ln(2)}{1.07} years
    why is it that you've used {1.07}??

    Shouldnt r be 1.017?? Or was just a human error? because if ln {2} / 1.07 < 1 than that will be a decay not growth wouldn't it?
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  5. #5
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    correct, I did use the wrong value.

    I hope displaying the methodology helped all the same...
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