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Math Help - Monthly growth rate with only double time given (exponential)

  1. #1
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    Monthly growth rate with only double time given (exponential)

    I have a question. I am not looking for the answer just the help to figure it out.

    Question is:

    "A towns population has doubled after 15 years, 3 months. what is monthly growth rate?"

    Any help is appreciated.
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  2. #2
    GJA
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    Re: Monthly growth rate with only double time given (exponential)

    Hi, robellard. You're right in your heading that it will involve exponentials; logarithms might also be useful too. Do you have any guess as to what the equation you should start with would be?
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  3. #3
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    Re: Monthly growth rate with only double time given (exponential)

    Well the section is focused on geometric sequences, and one formula they give for another problem is:

    tn = 26235 * 1.009^(n-1)

    I used logarithms to figure out the problem previous to this which is :

    "How long would it take for population of focus C (26235 - numbers above) to double.

    I am pretty sure it is to include logarithms as well, but I am unsure just how.
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    GJA
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    Re: Monthly growth rate with only double time given (exponential)

    You're right. To solve the previous problem logarithms would be used. I would look at the current problem in a way similar to the previous problem. Basically in the previous problem you knew the rate, but not the time and so you had something like

    2=(1.009)^{t},

    where you needed to solve for t. In this case you have a similar situation, only now you know t=183 and it's the rate you need to determine. Does that help give you a place to jump off from? Good luck!
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  5. #5
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    Re: Monthly growth rate with only double time given (exponential)

    I Would have done it as P(t)= P_0(2^{t/183}) where t is in months. You should be able to see why- if t= 183= 15*12+ 3 P(183)= P_0(2^1)= 2P_0. If t= 1 month, P(t)= P_0(2^{1/183})= 0.005464P_0.
    Last edited by HallsofIvy; August 5th 2012 at 03:22 PM.
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